Friedman ? « A free boundary problem for quasilinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.11, issue.4 1, pp.1-44, 1984. ,
Savaré ? Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, 2005. ,
The Valuation of American Options on Multiple Assets, Mathematical Finance, vol.7, issue.3, pp.241-286, 1997. ,
DOI : 10.1111/1467-9965.00032
Monneau ? « On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, 2005. ,
Perthame ? « Two-dimensional Keller- Segel : Optimal critical mass and qualitative properties of the solutions, 2005. ,
Caffarelli ? « A monotonicity formula for heat functions in disjoint domains », in Boundary value problems for partial differential equations and applications, RMA Res. Notes Appl. Math, vol.29, pp.53-60, 1993. ,
Competing symmetries, the logarithmic HLS inequality and Onofri's inequality ons n, Geometric and Functional Analysis, vol.102, issue.1, pp.90-104, 1992. ,
DOI : 10.1007/BF01895706
Percus ? « Nonlinear aspects of chemotaxis, Math. Biosci, vol.56, pp.3-4, 1981. ,
Shahgholian ? « Regularity of a free boundary in parabolic potential theory, Journal of the American Mathematical Society, vol.17, issue.04, pp.827-869, 2004. ,
DOI : 10.1090/S0894-0347-04-00466-7
Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions, Milan Journal of Mathematics, vol.72, issue.1, pp.1-29, 2004. ,
DOI : 10.1007/s00032-003-0026-x
Optimal critical mass in the two dimensional Keller???Segel model in, Comptes Rendus Mathematique, vol.339, issue.9, pp.611-616, 2004. ,
DOI : 10.1016/j.crma.2004.08.011
Sircar ? Derivatives in financial markets with stochastic volatility [Fri64] A. Friedman ? Partial differential equations of parabolic type, Parabolic variational inequalities in one space dimension and smoothness of the free boundary, pp.151-176, 1964. ,
Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis, Mathematische Nachrichten, vol.17, issue.1, pp.77-114, 1998. ,
DOI : 10.1002/mana.19981950106
On explosions of solutions to a system of partial differential equations modelling chemotaxis, Transactions of the American Mathematical Society, vol.329, issue.2, pp.819-824, 1992. ,
DOI : 10.1090/S0002-9947-1992-1046835-6
Segel ? « Initiation of slide mold aggregation viewed as an instability, no. 399 ?-415. [Lie96] G. M. Lieberman ? Second order parabolic differential equations, 1970. ,
Ural ceva ? Linear and quasilinear equations of parabolic type, Translated from the Russian by S, Smith. Translations of Mathematical Monographs, vol.23, 1967. ,
On the number of singularities for the obstacle problem in two dimensions, Journal of Geometric Analysis, vol.138, issue.4, pp.359-389, 2003. ,
DOI : 10.1007/BF02930701
The determination of spatial pattern inDictyostelium discoideum, Journal of Biosciences, vol.13, issue.4, pp.353-394, 1992. ,
DOI : 10.1007/BF02720094
Weinstein ? « Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys, vol.8783, issue.4, pp.567-576, 1982. ,
Samsoen ? « Estimation de la frontì ere libre des options américaines au voisinage de l'´ echéance, C. R. Acad. Sci. Paris Sér. I Math, issue.2, pp.316-171, 1993. ,
The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-659, 1973. ,
DOI : 10.1086/260062
CRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODEL, Mathematical Finance, vol.20, issue.3, pp.439-463, 2005. ,
DOI : 10.1023/A:1008699315785
URL : https://hal.archives-ouvertes.fr/hal-00693107
Friedman ? Variational principles and free-boundary problems, secondédsecondéd, 1988. ,
Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263-289, 1990. ,
DOI : 10.1007/BF00047211
Stampacchia ? An introduction to variational inequalities and their applications, Pure and Applied Mathematics, vol.88, 1980. ,
Lapeyre ? Introduction au calcul stochastique appliqué appliqué`appliquéà la finance, secondédsecondéd., EllipsesÉditionEllipses´EllipsesÉdition Marketing, 1997. ,
American option and the free boundary exercise region : a pde approach », Interfaces Free Bound, pp.79-98, 2005. ,
Asymptotics and calibration of local volatility models, Quantitative Finance, vol.4, issue.1, pp.61-69, 2002. ,
DOI : 10.1002/cpa.3160450103
Estimation de la frontì ere libre des options américaines au voisinage de l'´ echéance, C. R. Acad. Sci. Paris Sér. I Math, issue.2, pp.316-171, 1993. ,
On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00004421
Interest rate theory, Financial mathematics, pp.53-122, 1996. ,
CRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODEL, Mathematical Finance, vol.20, issue.3, pp.439-463, 2005. ,
DOI : 10.1023/A:1008699315785
URL : https://hal.archives-ouvertes.fr/hal-00693107
Regularity of a free boundary in parabolic potential theory, Journal of the American Mathematical Society, vol.17, issue.04, pp.827-869, 2004. ,
DOI : 10.1090/S0894-0347-04-00466-7
Applications of Malliavin calculus to Monte-Carlo methods in finance. II, Finance and Stochastics, vol.5, issue.2, pp.201-236, 2001. ,
DOI : 10.1007/PL00013529
Variational principles and free-boundary problems, secondédsecondéd, 1988. ,
Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, vol.11, issue.3, pp.215-260, 1981. ,
DOI : 10.1016/0304-4149(81)90026-0
Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263-289, 1990. ,
DOI : 10.1007/BF00047211
Critical price near maturity for an American option on a dividend-paying stock, Ann. Appl. Probab, vol.13, issue.2, pp.800-815, 2003. ,
Appendix: a free boundary problem for the heat equation arising from a problem in mathematical economics, Indust. Manage. Rev ,
American options and the free boundary exercise region: a PDE approach, Interfaces and Free Boundaries, vol.7, issue.1, pp.79-98, 2005. ,
DOI : 10.4171/IFB/114
Options américaines dans un modèle de black-scholes multidimensionnel, Thèse, 1999. ,
An optimal stopping problem with linear reward, Acta Mathematica, vol.132, issue.0, pp.111-151, 1974. ,
DOI : 10.1007/BF02392110
On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00004421
The regularity of free boundaries in higher dimensions, Acta Mathematica, vol.139, issue.0, pp.155-184, 1977. ,
DOI : 10.1007/BF02392236
Some New Monotonicity Theorems with Applications to Free Boundary Problems, The Annals of Mathematics, vol.155, issue.2, pp.369-404, 2002. ,
DOI : 10.2307/3062121
Regularity of a free boundary in parabolic potential theory, Journal of the American Mathematical Society, vol.17, issue.04, pp.827-869, 2004. ,
DOI : 10.1090/S0894-0347-04-00466-7
The structure of the singular set of a free boundary in potential theory ,
Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, 1969. ,
Friedman ? Variational principles and free-boundary problems, secondédsecondéd, 1988. ,
Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263-289, 1990. ,
DOI : 10.1007/BF00047211
Stampacchia ? An introduction to variational inequalities and their applications, Pure and Applied Mathematics, vol.88, 1980. ,
On the number of singularities for the obstacle problem in two dimensions, Journal of Geometric Analysis, vol.138, issue.4, pp.359-389, 2003. ,
DOI : 10.1007/BF02930701
American options and the free boundary exercise region: a PDE approach, Interfaces and Free Boundaries, vol.7, issue.1, pp.79-98, 2005. ,
DOI : 10.4171/IFB/114
Some examples of singularities in a free boundary, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.4, issue.4 1, pp.133-144, 1977. ,
Stein ? Singular integrals and differentiability properties of functions, 1970. ,
A homogeneity improvement approach to the obstacle problem, Inventiones Mathematicae, vol.138, issue.1, pp.23-50, 1999. ,
DOI : 10.1007/s002220050340
until present : the Keller-Segel model in chemotaxis and its consequences. I », Jahresber. Deutsch. Math.-Verein, vol.105, issue.3, pp.103-165, 1970. ,
Segel ? « Initiation of slide mold aggregation viewed as an instability, J. Theor. Biol, vol.26, issue.399, p.415, 1970. ,
The determination of spatial pattern inDictyostelium discoideum, Journal of Biosciences, vol.13, issue.4, pp.353-394, 1992. ,
DOI : 10.1007/BF02720094
Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research, References References, pp.35-43, 2004. ,
DOI : 10.1007/s00605-004-0239-2
The Thomas-Fermi-von Weizs??cker theory of atoms and molecules, Communications in Mathematical Physics, vol.27, issue.2, pp.167-180, 1981. ,
DOI : 10.1007/BF01942059
The Keller???Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion, SIAM Journal on Mathematical Analysis, vol.38, issue.4, pp.2005-098, 2005. ,
DOI : 10.1137/050637923
Steady states for Streater's energy-transport models of self-gravitating particles, IMA Volumes in Mathematics Series, vol.135, pp.1149-1162, 2001. ,
Perthame ? " Two-dimensional Keller- Segel: Optimal critical mass and qualitative properties of the solutions, 2005. ,
The 8?-problem for radially symmetric solutions of a chemotaxis model in a disc, 2005. ,
in two dimensions, Communications in Partial Differential Equations, vol.13, issue.8-9, pp.1223-1253, 1991. ,
DOI : 10.1007/BF02760233
A class of nonlocal parabolic problems occurring in statistical mechanics, Colloq. Math, vol.66, issue.1, pp.131-145, 1993. ,
Volume effects in the keller-segel model: energy estimates preventing blow-up, 2005. ,
Competing symmetries, the logarithmic HLS inequality and Onofri's inequality ons n, Geometric and Functional Analysis, vol.102, issue.1, pp.90-104, 1992. ,
DOI : 10.1007/BF01895706
A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Communications in Mathematical Physics, vol.187, issue.3, pp.501-525, 1992. ,
DOI : 10.1007/BF02099262
Kinetic Models for Chemotaxis and their Drift-Diffusion Limits, Monatshefte f???r Mathematik, vol.142, issue.1-2, pp.123-141, 2004. ,
DOI : 10.1007/s00605-004-0234-7
A chemotaxis model motivated by angiogenesis, Comptes Rendus Mathematique, vol.336, issue.2, pp.141-146, 2003. ,
DOI : 10.1016/S1631-073X(02)00008-0
Cattaneo models for chemosensitive movement, Journal of Mathematical Biology, vol.46, issue.5, pp.153-170, 2003. ,
DOI : 10.1007/s00285-003-0222-x
A remark on the critical explosion parameter for a semilinear elliptic equation in a generic domain using an explosion time of an ordinary differential equation, Nonlinear Analysis: Theory, Methods & Applications, vol.24, issue.8, pp.1149-1162, 1995. ,
DOI : 10.1016/0362-546X(94)00220-C
Symmetry and related properties via the maximum principle, Communications in Mathematical Physics, vol.43, issue.3, pp.209-243, 1979. ,
DOI : 10.1007/BF01221125
Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis, Mathematische Nachrichten, vol.17, issue.1, pp.77-114, 1998. ,
DOI : 10.1002/mana.19981950106
Some properties of fractional integrals. I., Mathematische Zeitschrift, vol.62, issue.2, pp.565-606, 1928. ,
DOI : 10.1007/BF01171116
Finite-time aggregation into a single point in a reaction - diffusion system, Nonlinearity, vol.10, issue.6, pp.1739-1754, 1997. ,
DOI : 10.1088/0951-7715/10/6/016
Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding, Advances in Applied Mathematics, vol.26, issue.4, pp.280-301, 2001. ,
DOI : 10.1006/aama.2001.0721
Finite sampling radius in chemotaxis, 2005. ,
Boundedness vs. blow-up in a chemotaxis system, Journal of Differential Equations, vol.215, issue.1, pp.52-107, 2005. ,
DOI : 10.1016/j.jde.2004.10.022
On explosions of solutions to a system of partial differential equations modelling chemotaxis, Transactions of the American Mathematical Society, vol.329, issue.2, pp.819-824, 1992. ,
DOI : 10.1090/S0002-9947-1992-1046835-6
Segel ? " Model for chemotaxis, J. Theor. Biol, vol.30, pp.225-234, 1971. ,
Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math, issue.2 2, pp.118-349, 1983. ,
Applications of mathematical modelling to biological pattern formation, Coherent structures in complex systems, pp.205-217, 2001. ,
Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis, Adv. Math. Sci. Appl, vol.8, issue.1, pp.145-156, 1998. ,
Keller-Segel system and the concentration lemma, Variational problems and related topics (Japanese), pp.75-80, 1997. ,
Aggregation, blowup, and collapse: the ABCs of taxis in reinforced random walks, SIAM J. Appl. Math, vol.57, issue.4, pp.1044-1081, 1997. ,
Metastability in Chemotaxis Models, Journal of Dynamics and Differential Equations, vol.105, issue.3, pp.293-330, 2005. ,
DOI : 10.1007/s10884-005-2938-3
Quorum sensing models in chemotaxis, 2005. ,
Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.2, issue.5 2, pp.395-431, 2003. ,
Finite time blow-up in some models of chemotaxis, Journal of Mathematical Biology, vol.33, issue.4, pp.388-414, 1995. ,
DOI : 10.1007/BF00176379
Time global solutions to a parabolic-elliptic system modelling chemotaxis, Asymptot. Anal, vol.32, issue.1, pp.63-89, 2002. ,
Fractional step methods applied to a chemotaxis model, Journal of Mathematical Biology, vol.41, issue.5, pp.455-475, 2000. ,
DOI : 10.1007/s002850000038
Stability of some mechanisms of chemotactic aggregation, SIAM J. Appl. Math, vol.62, issue.5, pp.1581-1633, 2002. ,
Achdou, An inverse problem for a parabolic variational inequality arising in volatility calibration with American options, SIAM J. Control Optim, vol.43, pp.1583-1615, 2005. ,
A free boundary problem for quasilinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, issue.4, pp.11-12, 1984. ,
Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, 2005. ,
Entropies and equilibria of many-particle systems: an essay on recent research, Monatsh. Math, pp.142-177, 2004. ,
Théorie de la spéculation, Les Grands Classiques Gauthier-Villars. [Gauthier-Villars Great Classics, Editions Jacques Gabay, 1995. ,
Estimation de lafrontì ere libre des options américaines au voisinage de l'´ echéance, C. R. Acad. Sci. Paris Sér. I Math, pp.316-171, 1993. ,
Sharp Sobolev Inequalities on the Sphere and the Moser--Trudinger Inequality, The Annals of Mathematics, vol.138, issue.1, pp.213-242, 1993. ,
DOI : 10.2307/2946638
The Thomas-Fermi-von Weizs??cker theory of atoms and molecules, Communications in Mathematical Physics, vol.27, issue.2, pp.167-180, 1981. ,
DOI : 10.1007/BF01942059
On the theory of option pricing, Acta Appl. Math, vol.2, pp.139-158, 1984. ,
Applications des inéquations variationnelles en contrôle stochastique, Méthodes Mathématiques de l'Informatique, 1978. ,
Asymptotics and calibration of local volatility models, Quantitative Finance, vol.4, issue.1, pp.61-69, 2002. ,
DOI : 10.1002/cpa.3160450103
Lévy processes, Cambridge Tracts in Mathematics, vol.121, 1996. ,
Local and global solvability of some parabolic systems modelling chemotaxis, Adv. Math. Sci. Appl, vol.8, pp.715-743, 1998. ,
Steady States for Streater???s Energy-Transport Models of Self-Gravitating Particles, IMA Volumes in Mathematics Series, p.135, 2001. ,
DOI : 10.1007/978-1-4613-0017-5_2
The 8?-problem for radially symmetric solutions of a chemotaxis model in a disc, 2005. ,
A class of nonlocal parabolic problems occurring in statistical mechanics, Colloq. Math, vol.66, pp.131-145, 1993. ,
Interest rate theory, Financial mathematics, pp.53-122, 1996. ,
DOI : 10.1016/0304-405X(77)90016-2
The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-659, 1973. ,
DOI : 10.1086/260062
On the regularity of the free boundary in the parabolic obstacle problem. Application to American options, Nonlinear Analysis: Theory, Methods & Applications, vol.65, issue.7, 2005. ,
DOI : 10.1016/j.na.2005.10.009
On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00004421
Perthame, Two-dimensional Keller-Segel: Optimal critical mass and qualitative properties of the solutions, 2005. ,
Théorie et applications. [Theory and applications]. [29] H. Brezis et F. Merle, Uniform estimates and blow-up behavior for solutions of ??u = V (x)e u in two dimensions, Collection Mathématiques Appliquées pour la Ma??triseMa??trise. [Collection of Applied Mathematics for the Master's Degree] Comm. Partial Differential Equations, pp.16-1223, 1983. ,
The Valuation of American Options on Multiple Assets, Mathematical Finance, vol.7, issue.3, pp.241-286, 1997. ,
DOI : 10.1111/1467-9965.00032
The Keller???Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion, SIAM Journal on Mathematical Analysis, vol.38, issue.4, pp.2005-098, 2005. ,
DOI : 10.1137/050637923
The regularity of free boundaries in higher dimensions, Acta Mathematica, vol.139, issue.0, pp.155-184, 1977. ,
DOI : 10.1007/BF02392236
Compactness methods in free boundary problems, Communications in Partial Differential Equations, vol.28, issue.2, pp.427-448, 1980. ,
DOI : 10.1080/0360530800882144
A monotonicity formula for heat functions in disjoint domains, in Boundary value problems for partial differential equations and applications, RMA Res. Notes Appl. Math, vol.29, pp.53-60, 1993. ,
Some New Monotonicity Theorems with Applications to Free Boundary Problems, The Annals of Mathematics, vol.155, issue.2, pp.155-369, 2002. ,
DOI : 10.2307/3062121
Regularity of a free boundary in parabolic potential theory, Journal of the American Mathematical Society, vol.17, issue.04, pp.827-869, 2004. ,
DOI : 10.1090/S0894-0347-04-00466-7
The structure of the singular set of a free boundary in potential theory ,
A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Communications in Mathematical Physics, vol.187, issue.3, pp.501-525, 1992. ,
DOI : 10.1007/BF02099262
Competing symmetries, the logarithmic HLS inequality and Onofri's inequality ons n, Geometric and Functional Analysis, vol.102, issue.1, pp.90-104, 1992. ,
DOI : 10.1007/BF01895706
Volume effects in the keller-segel model: energy estimates preventing blow-up, tech. rep, 2005. ,
Kinetic Models for Chemotaxis and their Drift-Diffusion Limits, Monatshefte f???r Mathematik, vol.142, issue.1-2, pp.123-141, 2004. ,
DOI : 10.1007/s00605-004-0234-7
CRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODEL, Mathematical Finance, vol.20, issue.3, pp.439-463, 2005. ,
DOI : 10.1023/A:1008699315785
URL : https://hal.archives-ouvertes.fr/hal-00693107
Nonlinear aspects of chemotaxis, Mathematical Biosciences, vol.56, issue.3-4, pp.217-237, 1981. ,
DOI : 10.1016/0025-5564(81)90055-9
A chemotaxis model motivated by angiogenesis, Comptes Rendus Mathematique, vol.336, issue.2, pp.141-146, 2003. ,
DOI : 10.1016/S1631-073X(02)00008-0
Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar, vol.2, pp.299-318, 1967. ,
Cattaneo models for chemosensitive movement, Journal of Mathematical Biology, vol.46, issue.2, pp.153-170, 2003. ,
DOI : 10.1007/s00285-002-0173-7
Cattaneo models for chemosensitive movement, Journal of Mathematical Biology, vol.46, issue.2, pp.153-170, 2003. ,
DOI : 10.1007/s00285-002-0173-7
Kinetic models for chemotaxis: hydrodynamic limits and the back-of-the-wave problem, tech. rep, pp.2003-102, 2003. ,
Optimal critical mass in the two dimensional Keller???Segel model in, Comptes Rendus Mathematique, vol.339, issue.9, pp.339-611, 2004. ,
DOI : 10.1016/j.crma.2004.08.011
A remark on the critical explosion parameter for a semilinear elliptic equation in a generic domain using an explosion time of an ordinary differential equation, Nonlinear Anal, pp.1149-1162, 1995. ,
Some Theorems About the Riesz Fractional Integral, Transactions of the American Mathematical Society, vol.80, issue.1, pp.124-134, 1955. ,
DOI : 10.2307/1993008
Pricing and hedging with smiles, Mathematics of derivative securities, pp.103-111, 1995. ,
Optimal stopping with random intervention times, Advances in Applied Probability, vol.III, issue.01, pp.141-157, 2002. ,
DOI : 10.1086/296288
Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, 1969. ,
Derivatives in financial markets with stochastic volatility, 2000. ,
Applications of Malliavin calculus to Monte-Carlo methods in finance. II, Finance Stoch, pp.201-236, 2001. ,
Partial differential equations of parabolic type, N.J, 1964. ,
Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis, Mathematische Nachrichten, vol.17, issue.1, pp.77-114, 1998. ,
DOI : 10.1002/mana.19981950106
Symmetry and related properties via the maximum principle, Communications in Mathematical Physics, vol.43, issue.3, pp.209-243, 1979. ,
DOI : 10.1007/BF01221125
Asymptotically self-similar blow-up of semilinear heat equations, Communications on Pure and Applied Mathematics, vol.38, issue.3, pp.297-319, 1985. ,
DOI : 10.1002/cpa.3160380304
HYDRODYNAMIC LIMIT FOR THE VLASOV???POISSON???FOKKER???PLANCK SYSTEM: ANALYSIS OF THE TWO-DIMENSIONAL CASE, Mathematical Models and Methods in Applied Sciences, vol.15, issue.05, pp.737-752, 2005. ,
DOI : 10.1142/S021820250500056X
URL : https://hal.archives-ouvertes.fr/hal-00018817
Logarithmic Sobolev Inequalities, American Journal of Mathematics, vol.97, issue.4, pp.1061-1083, 1975. ,
DOI : 10.2307/2373688
Some properties of fractional integrals. I., Mathematische Zeitschrift, vol.62, issue.2, pp.565-606, 1928. ,
DOI : 10.1007/BF01171116
Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process, Appl, vol.11, pp.215-260, 1981. ,
Finite-time aggregation into a single point in a reaction - diffusion system, Nonlinearity, vol.10, issue.6, pp.10-1739, 1997. ,
DOI : 10.1088/0951-7715/10/6/016
Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding, Advances in Applied Mathematics, vol.26, issue.4, pp.280-301, 2001. ,
DOI : 10.1006/aama.2001.0721
Finite sampling radius in chemotaxis, tech. rep., in preparation, 2005. ,
On the existence of radially symmetric blow-up solutions for the Keller-Segel model, Journal of Mathematical Biology, vol.44, issue.5, pp.463-478, 2002. ,
DOI : 10.1007/s002850100134
From 1970 until present: the keller-segel model in chemotaxis and its consequences, Max-Planck-Institut fur Mathematik in den Naturwissenschatften Leipzig, 2003. ,
From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. I, Jahresber, Deutsch. Math.-Verein, vol.105, pp.103-165, 2003. ,
Boundedness vs. blow-up in a chemotaxis system, Journal of Differential Equations, vol.215, issue.1, pp.52-107, 2005. ,
DOI : 10.1016/j.jde.2004.10.022
On explosions of solutions to a system of partial differential equations modelling chemotaxis, Transactions of the American Mathematical Society, vol.329, issue.2, pp.819-824, 1992. ,
DOI : 10.1090/S0002-9947-1992-1046835-6
Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263-289, 1990. ,
DOI : 10.1007/BF00047211
On the pricing of American options, Applied Mathematics & Optimization, vol.60, issue.1, pp.37-60, 1988. ,
DOI : 10.1007/BF01448358
Initiation of slide mold aggregation viewed as an instability, J. Theor. Biol, p.26, 1970. ,
An introduction to variational inequalities and their applications, of Pure and Applied Mathematics, 1980. ,
DOI : 10.1137/1.9780898719451
On the convergence of discrimination information, IEEE Trans. Information Theory, pp.14-765, 1968. ,
Ural ceva, Linear and quasilinear equations of parabolic type, Translated from the Russian by S, Smith. Translations of Mathematical Monographs, vol.23, 1967. ,
Introduction au calcul stochastique appliquéappliqué`appliquéà la finance, EllipsesÉditionEllipses´EllipsesÉdition Marketing, 1997. ,
Critical price near maturity for an American option on a dividend-paying stock, Ann. Appl. Probab, vol.13, pp.800-815, 2003. ,
FROM THE NONLOCAL TO THE LOCAL DISCRETE DIFFUSIVE COAGULATION EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.12, issue.07, pp.1035-1048, 2002. ,
DOI : 10.1142/S021820250200201X
Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math, issue.2, pp.118-349, 1983. ,
Second order parabolic differential equations, 1996. ,
DOI : 10.1142/3302
Wave propagation in the early stages f aggregation of cellular slime molds, J. theor. Biol, pp.31-101, 1971. ,
Applications of Mathematical Modelling to Biological Pattern Formation, Lecture Notes in Phys, vol.567, pp.205-217, 2001. ,
DOI : 10.1007/3-540-44698-2_13
Numerical simulation of chemotactic bacteria aggregation via mixed finite elements, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.4, pp.617-630, 2003. ,
DOI : 10.1051/m2an:2003048
Appendix: a free boundary problem for the heat equation arising from a problem in mathematical economics, Indust. Manage. Rev, vol.6, pp.32-39, 1965. ,
On the number of singularities for the obstacle problem in two dimensions, Journal of Geometric Analysis, vol.138, issue.4, pp.359-389, 2003. ,
DOI : 10.1007/BF02930701
Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis, Adv. Math. Sci. Appl, vol.8, pp.145-156, 1998. ,
Keller-Segel system and the concentration lemma, S¯ urikaisekikenky¯ usho K¯ oky¯ uroku, Variational problems and related topics (Japanese), pp.75-80, 1997. ,
Symmetry results for semilinear elliptic equations in R2, Proceedings of the Third World Congress of Nonlinear Analysts, Part, pp.3661-3670, 2001. ,
DOI : 10.1016/S0362-546X(01)00486-2
Self-similar solutions to a nonlinear parabolic-elliptic system, Proceedings of Third East Asia Partial Differential Equation Conference, pp.43-55, 2004. ,
The determination of spatial pattern inDictyostelium discoideum, Journal of Biosciences, vol.13, issue.4, pp.353-394, 1992. ,
DOI : 10.1007/BF02720094
Statistical mechanics of the N-point vortex system with random intensities on a bounded domain, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.21, issue.3, pp.381-399, 2004. ,
DOI : 10.1016/j.anihpc.2003.05.002
Aggregation, blowup, and collapse: the ABCs of taxis in reinforced random walks, SIAM J. Appl. Math, vol.57, pp.1044-1081, 1997. ,
Random walk with persistence and external bias, The Bulletin of Mathematical Biophysics, vol.198, issue.3, pp.311-338, 1953. ,
DOI : 10.1007/BF02476407
Non-existence of global solutions to Euler-Poisson equations for repulsive forces, Japan Journal of Applied Mathematics, vol.101, issue.2, pp.363-367, 1990. ,
DOI : 10.1007/BF03167849
Optimal stopping of controlled jump diffusion processes: a viscosity solution approach, J. Math. Systems Estim. Control, vol.8, p.27, 1998. ,
Metastability in Chemotaxis Models, Journal of Dynamics and Differential Equations, vol.105, issue.3, pp.293-330, 2005. ,
DOI : 10.1007/s10884-005-2938-3
American options and the free boundary exercise region: a PDE approach, Interfaces and Free Boundaries, vol.7, pp.79-98, 2005. ,
DOI : 10.4171/IFB/114
Finite time blow-up in some models of chemotaxis, Journal of Mathematical Biology, vol.33, issue.4, pp.388-414, 1995. ,
DOI : 10.1007/BF00176379
Quorum sensing models in chemotaxis, tech. rep., in preparation, 2005. ,
Obstacle problems in mathematical physics, p.114, 1987. ,
Probl??me de Cauchy pour une ??quation parabolique mod??lisant la relaxation des syst??mes stellaires auto-gravitants, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.10, pp.903-908, 2001. ,
DOI : 10.1016/S0764-4442(01)01932-2
Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.2, issue.5, pp.395-431, 2003. ,
Some examples of singularities in a free boundary, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.4, issue.4, pp.133-144, 1977. ,
Time global solutions to a parabolic-elliptic system modelling chemotaxis, Asymptot. Anal, vol.32, pp.63-89, 2002. ,
Compact sets in the space L p (0, Ann. Mat. Pura Appl, issue.4, pp.146-65, 1987. ,
On a theorem of functional analysis (russian), Mat. Sb. (N.S.), vol.4, pp.471-479, 1938. ,
Singular integrals and differentiability properties of functions, 1970. ,
The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems, SIAM Journal on Applied Mathematics, vol.61, issue.1, pp.183-212, 2000. ,
DOI : 10.1137/S0036139998342065
Free energy and self-interacting particles, Progress in Nonlinear Differential Equations and their Applications, 2005. ,
Fractional step methods applied to a chemotaxis model, Journal of Mathematical Biology, vol.41, issue.5, pp.41-455, 2000. ,
DOI : 10.1007/s002850000038
An optimal stopping problem with linear reward, Acta Mathematica, vol.132, issue.0, pp.111-151, 1974. ,
DOI : 10.1007/BF02392110
Stability of Some Mechanisms of Chemotactic Aggregation, SIAM Journal on Applied Mathematics, vol.62, issue.5, pp.1581-1633, 2002. ,
DOI : 10.1137/S0036139900380049
Options américaines dans un modèle de Black-Scholes multidimensionnel, 1999. ,
Models of phase transitions, Progress in Nonlinear Differential Equations and their Applications, 1996. ,
Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys, vol.8783, pp.567-576, 1982. ,
DOI : 10.1007/bf01208265
A homogeneity improvement approach to the obstacle problem, Inventiones Mathematicae, vol.138, issue.1, pp.23-50, 1999. ,
DOI : 10.1007/s002220050340
Analytic extensions of differentiable functions defined in closed sets, Transactions of the American Mathematical Society, vol.36, issue.1, pp.63-89, 1934. ,
DOI : 10.1090/S0002-9947-1934-1501735-3
The heat equation, Pure and Applied Mathematics, vol.67, 1975. ,
Long time behaviour of solutions to a chemotaxis model with volume filling effect, Hyke preprint server, p.166, 2004. ,