, An exactly solvable model of subdiusionreaction front propagation, 2013.
, Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications: Cetraro, Italy 2011, volume 2074 of Lecture notes in mathematics, 2013.
, Analyse numérique et optimisation : Une introduction à la modélisation mathématique et à la simulation numérique. Editions de l'Ecole Polytechnique, 2012.
, Entropies and equilibria of many-particle systems: An essay on recent research, Monatshefte für Mathematik, vol.142, issue.12, p.3543, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01583063
, Improved entropy decay estimates for the heat equation, Journal of Mathematical Analysis and Applications, vol.343, issue.1, p.190206, 2008.
DOI : 10.1016/j.jmaa.2008.01.046
, ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS, Communications in Partial Differential Equations, vol.324, issue.1-2, p.43100, 2001.
DOI : 10.1007/s002200050631
, Nonlinear diusion in population genetics, combustion , and nerve pulse propagation, Lecture Notes in Math, vol.446, p.549, 1975.
, Multidimensional nonlinear diusion arising in population genetics, Adv. in Math, vol.30, issue.1, p.3376, 1978.
, Anomalous Diusion of Proteins Due to Molecular Crowding, Biophysics Journal, vol.89, p.29602971, 2005.
, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Modern Birkhäuser Classics, Birkhäuser Basel, 1997.
, Solutions de viscosité des équations de Hamilton-Jacobi, 1994.
, Improved intermediate asymptotics for the heat equation, Applied Mathematics Letters, vol.24, issue.1, p.7681, 2011.
DOI : 10.1016/j.aml.2010.08.020
URL : https://hal.archives-ouvertes.fr/hal-00409935
, Kinetische behandlung der keimbildung in übersättigten dämpfen, Annalen der Physik, vol.416, issue.8, p.719752, 1935.
DOI : 10.1002/andp.19354160806
, Anomalous diusion due to hindering by mobile obstacles undergoing brownian motion or orstein-ulhenbeck processes, Physical Review E, vol.89, issue.2, 2014.
DOI : 10.1103/physreve.89.022708
URL : http://arxiv.org/pdf/1103.2206
, Quantitative convergence towards a self-similar prole in an age-structured renewal equation for subdiusion, Acta Appl. Math, vol.145, p.1545, 2016.
, Intermediate asymptotics in L 1 for general nonlinear diusion equations, Applied Mathematics Letters, vol.15, issue.1, p.101107, 2002.
, Regular Variation, 1987.
DOI : 10.1017/CBO9780511721434
, Lectures on Gas Theory (Dover Books on Physics) Dover Books on Physics, 1964.
, Further Studies on the Thermal Equilibrium of Gas Molecules (1872), chapter 2.2. History of modern physical sciences, 2003.
, Kinetic Equations and Asymptotic Theory, Editions Scientiques Et, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00538692
, A kinetic eikonal equation, Comptes Rendus Mathematique, vol.350, issue.5-6, p.243248, 2012.
DOI : 10.1016/j.crma.2012.03.009
URL : https://hal.archives-ouvertes.fr/hal-00668874
, A Hamilton???Jacobi approach for a model of population structured by space and trait, Communications in Mathematical Sciences, vol.13, issue.6, p.14311452, 2015.
DOI : 10.4310/CMS.2015.v13.n6.a4
URL : https://hal.archives-ouvertes.fr/hal-00849406
, Large deviations for velocity-jump processes and non-local hamilton-jacobi equations, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01344939
, La mécanique ondulatoire de schrödinger: une méthode générale de resolution par approximations successives, Comptes Rendus de l'Academie des Sciences, pp.24-26, 1926.
, Transient Anomalous Diusion of Telomeres in the Nucleus of Mammalian Cells, Physical Review Letters, vol.103, p.14, 2009.
, Large deviations of a velocity jump process with a Hamilton???Jacobi approach, Comptes Rendus Mathematique, vol.355, issue.2
DOI : 10.1016/j.crma.2016.12.011
URL : https://hal.archives-ouvertes.fr/hal-01625774
, Chemotactic waves of bacteria at the mesoscale, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01340375
, Limiting
URL : https://hal.archives-ouvertes.fr/hal-01372949
, Pattern formation in a ux limited reactiondiusion equation of porous media type, Inventiones mathematicae, vol.206, issue.1, p.57108, 2016.
, The Mathematical Theory of Dilute Gases, 1994.
DOI : 10.1007/978-1-4419-8524-8
, Functional Analysis, Calculus of Variations and Optimal Control (Graduate Texts in Mathematics), 2013.
, Über die Art der Bewegung, welche wir Wärme nennen, Annalen der Physik und Chemie, vol.176, issue.3, p.353380, 1857.
DOI : 10.1002/andp.18571760302
, Frederic Poupaud, and Alexis Vasseur. Some Recent Results on the Kinetic Theory of Phase Transitions, p.103120, 2004.
, The Cell: A Molecular Approach, 2015.
, Two approximations of solutions of Hamilton-Jacobi equations, Mathematics of Computation, vol.43, issue.167, p.119, 1984.
DOI : 10.1090/S0025-5718-1984-0744921-8
, Viscosity solutions of Hamilton-Jacobi equations . Transactions of the, p.11, 1983.
, Diusion and Reactions in Fractals and Disordered Systems, 2010.
, A Guide to Monte Carlo Simulations in Statistical Physics, 2005.
, Probing short-range protein Brownian motion in the cytoplasm of living cells, Nature Communications, vol.15, p.5891, 2014.
DOI : 10.1038/sj.mt.6300172
, Entropy methods and nonlinear diusions Available at https, 2012.
, Entropy and linear diusion equations Available at https, 2012.
, Renewal theory from the point of view of the theory of probability. Transactions of the, p.422422, 1948.
, Markov jump processes, Teor. Veroyatnost. i Primenen, vol.3, p.4160, 1958.
, Some limit theorems for sums of independent random variables with innite mathematical expectations, In Select. Transl. Math. Statist. and Probability Inst. Math. Statist. and Amer. Math. Soc, vol.1, p.171189, 1961.
, Zur Theorie der Brownschen Bewegung. (German) [On the theory of Brownian motion], p.371381, 1906.
, Über die von der molekularkinetischen Theorie der Wärme gefordert Bewegung von in ruhenden Flüÿigkeiten suspendierten Teilchen. (German) [On the molecularkinetic theory of the movement by heat of particles suspended in liquids at rest], pp.549-560, 1905.
DOI : 10.1002/andp.19053220806
URL : http://sedici.unlp.edu.ar/bitstream/handle/10915/2785/Documento_completo__.pdf?sequence=1
, Cell biology: Join the crowd, Nature, issue.6953, p.4252728, 2003.
DOI : 10.1038/425027a
, The perturbed test function method for viscosity solutions of nonlinear PDE, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.111, pp.3-4359375, 1989.
, Partial Dierential Equations: Second Edition (Graduate Studies in Mathematics), 2010.
, A pde approach to geometric optics for certain semilinear parabolic equations, Indiana University Mathematics Journal, vol.38, issue.1, 1989.
, Subdiusive transport in non-homogeneous media and nonlinear fractional equations, 2015.
, Control and Filtering for Semi-Markovian Jump Systems. Studies in Systems, Decision and Control 81, 2017.
, The Johnson-Mehl-Avrami-Kolmogorov model: A brief review, Il Nuovo Cimento D, vol.20, issue.7, p.11711182, 1998.
, Non-homogeneous Random Walks, Subdiffusive Migration of Cells and Anomalous Chemotaxis, Mathematical Modelling of Natural Phenomena, vol.371, issue.1, p.2843, 2013.
DOI : 10.1098/rsta.2012.0179
, Subdiusive master equation with space-dependent anomalous exponent and structural instability, Physical Review E, vol.85, p.16, 2012.
DOI : 10.1103/physreve.85.031132
URL : https://www.research.manchester.ac.uk/portal/files/52849023/falconer.pdf
, Nonlinear degradation-enhanced transport of morphogens performing subdiffusion, Physical Review E, vol.89, issue.1, p.12107, 2014.
DOI : 10.1103/PhysRevLett.100.108304
, On the Integral Equation of Renewal Theory, The Annals of Mathematical Statistics, vol.12, issue.3, pp.243-267, 1941.
DOI : 10.1214/aoms/1177731708
, On the Integral Equation of Renewal Theory, 1941.
, An Introduction to Probability Theory and Its Applications, volume II, 1966.
, Ueber diusion, Annalen der Physik, vol.170, issue.1, pp.5986-1855
, The approach of solutions of nonlinear diusion equations to travelling front solutions, Arch. Ration. Mech. Anal, vol.65, issue.4, p.335361, 1977.
, THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.355-369, 1937.
DOI : 10.1111/j.1469-1809.1937.tb02153.x
, Controlled Markov processes and viscosity solutions , volume 25 of Stochastic Modelling and Applied Probability, 2006.
, Éditions Jacques Gabay, 1822. [65] M. I. Freidlin. Geometric optics approach to reaction-diusion equations, SIAM Journal on Applied Mathematics, vol.46, issue.2, p.222232, 1986.
, reaction under subdiffusion, Physical Review E, vol.41, issue.3, p.31101, 2011.
DOI : 10.1103/PhysRevE.63.056103
, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics, 1996.
DOI : 10.1137/1.9781611971477
, Physical Nature of Bacterial Cytoplasm, Physical Review Letters, vol.88, issue.9, p.14, 2006.
DOI : 10.1063/1.1341926
, Hydrodynamic limits of kinetic models In Topics in kinetic theory, Fields Inst. Commun. Amer. Math. Soc, vol.46, p.175, 2005.
, Sampling the cell with anomalous diusionthe discovery of slowness, Biophysical Journal, vol.94, issue.1, p.9094, 2008.
, Stopped random walks: limit theorems and applications. Springer Series in Operations Research and Financial Engineering, 2009.
, Invariants and exponential rate of convergence to steady state in the renewal equation. Markov Process, p.413424, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00113528
, New Models of the Cell Nucleus: Crowding, Entropic Forces, Phase Separation, and Fractals, International Review of Cell and Molecular Biology, p.307, 2013.
, Brownian motors, Annalen der Physik, vol.182, issue.9, pp.51-70, 2005.
DOI : 10.1002/1521-396X(200011)182:1<585::AID-PSSA585>3.0.CO;2-4
, Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, vol.71, issue.2, pp.231-303, 1987.
DOI : 10.1016/0021-9991(87)90031-3
, Uniformly high-order accurate nonoscillatory schemes. I
DOI : 10.1007/978-3-642-60543-7_11
URL : http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA158177&Location=U2&doc=GetTRDoc.pdf
, Diusion in disordered media Advances in Physics, p.695798, 1987.
, Anomalous diusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diusion equations
, Anomalous transport in the crowded world of biological cells, Reports on Progress in Physics, vol.76, issue.4, p.46602, 2013.
, Anomalous transport in the crowded world of biological cells, Reports on Progress in Physics, vol.76, issue.4, p.46602, 2013.
, A revisited
, Morphogen gradient formation in a complex environment: An anomalous diffusion model, Physical Review E, vol.128, issue.4, pp.1-10, 2005.
DOI : 10.1029/2003WR002750
, Renewal Theory for Perturbed Random Walks and Similar Processes. Probability and Its Applications, Birkhäuser Basel, 2016.
DOI : 10.1007/978-3-319-49113-4
, Mathematical Modeling in Systems Biology
, Nouvelles Expériences et Observations Sur Divers Objets De Physique, 1784.
, Author response, eLife, vol.81, 2014.
DOI : 10.7554/eLife.02230.028
, On certain approximate solutions of lineae dierential equations of the second order, Proceedings of the London Mathematical Society, pp.2-23428436, 1925.
, Ecient implementation of weighted eno schemes, Journal of computational Physics, issue.126, p.202228, 1996.
, Weighted ENO Schemes for Hamilton--Jacobi Equations, SIAM Journal on Scientific Computing, vol.21, issue.6, p.21262143, 2000.
DOI : 10.1137/S106482759732455X
, Nucleation and growth in one dimension. II. Application to DNA replication kinetics, Physical Review E, vol.38, issue.1, p.11909, 2005.
DOI : 10.1143/JPSJ.61.1919
, Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami model, Physical Review E, vol.62, issue.1, p.11908, 2005.
DOI : 10.1083/jcb.152.1.15
, Research of the equation of the diusion connected to increase of quantity of substance, and its application to one biological problem, Bulletin of the Moscow State University, vol.1, issue.6, p.126, 1937.
, Wellenmechanik und halbzahlige quantisierung. Zeitschrift für Physik, p.828840, 1926.
DOI : 10.1007/bf01451751
, Some Limit Theorems for Stochastic Processes, Indiana University Mathematics Journal, vol.7, issue.3, p.433448, 1958.
DOI : 10.1512/iumj.1958.7.57027
URL : http://www.iumj.indiana.edu/IUMJ/FTDLOAD/1958/7/57027/pdf
, An Invariance Principle in Renewal Theory, The Annals of Mathematical Statistics, vol.33, issue.2, p.685696, 1962.
DOI : 10.1214/aoms/1177704590
URL : http://doi.org/10.1214/aoms/1177704590
, Mouvement brownien, martingales et calcul stochastique, of Mathématiques & Applications (Berlin) [Mathematics & Applications
DOI : 10.1007/978-3-642-31898-6
, The kinetics of precipitation from supersaturated solid solutions, Journal of Physics and Chemistry of Solids, vol.19, issue.1-2, p.3550, 1961.
DOI : 10.1016/0022-3697(61)90054-3
, A non-markovian phase space approach to schrödinger dynamics: The space-time Wigner transform, Multiscale Modeling & Simulation, vol.14, issue.1, pp.430-451, 2016.
, A Contribution to the Theory of Self-Renewing Aggregates, With Special Reference to Industrial Replacement, The Annals of Mathematical Statistics, vol.10, issue.1, p.125, 1939.
DOI : 10.1214/aoms/1177732243
, De Rerum Natura
DOI : 10.1093/oseo/instance.00089507
, Elucidating anomalous protein diusion in living cells with uorescence correlation spectroscopyfacts and pitfalls, Journal of Fluorescence, vol.20, issue.1, p.1926, 2009.
DOI : 10.1007/s10895-009-0517-4
, Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Transactions on Modeling and Computer Simulation, vol.8, issue.1, p.330, 1998.
DOI : 10.1145/272991.272995
URL : http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf
, Operator renewal theory and mixing rates for dynamical systems with innite measure, Inventiones Mathematicae, issue.189, p.61110, 2012.
DOI : 10.1007/s00222-011-0361-4
URL : http://arxiv.org/pdf/1008.4113
, ReactionTransport Systems, 2010.
, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, vol.339, issue.1, pp.1-77, 2000.
DOI : 10.1016/S0370-1573(00)00070-3
, Anomalous diusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking, Phys. Chem. Chem. Phys, issue.44, p.162412824164, 2014.
, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, Journal of Physics A: Mathematical and General, vol.37, issue.31, p.161, 2004.
DOI : 10.1088/0305-4470/37/31/R01
, General relative entropy inequality: an illustration on growth models, Journal de Math??matiques Pures et Appliqu??es, vol.84, issue.9, p.12351260, 2005.
DOI : 10.1016/j.matpur.2005.04.001
URL : https://doi.org/10.1016/j.matpur.2005.04.001
, General relative entropy inequality: an illustration on growth models, Journal de Math??matiques Pures et Appliqu??es, vol.84, issue.9, 2005.
DOI : 10.1016/j.matpur.2005.04.001
URL : https://doi.org/10.1016/j.matpur.2005.04.001
, Mesoscopic modeling of stochastic reaction-diusion kinetics in the subdiusive regime
, STABILITY IN A NONLINEAR POPULATION MATURATION MODEL, Mathematical Models and Methods in Applied Sciences, vol.12, issue.12, p.17511772, 2002.
DOI : 10.1016/0022-5193(83)90024-3
, Singular limits for reaction-diusion equations with fractional laplacian and local or nonlocal nonlinearity, Communications in Partial Dierential Equations, vol.40, issue.5, p.957993, 2015.
, Random walks on lattices. II, Journal of Mathematical Physics, vol.6, issue.2, p.167181, 1965.
, Regular variation. Encyclopedia of mathematics and its applications 27, 1987.
, Weighted fast diusion equations (part II): Sharp asymptotic rates of convergence in relative error by entropy methods. Kinetic and Related Models, p.6191, 2016.
, Mathematical modelling of subdiusion-reaction systems, Mathematical Modelling of Natural Phenomena, vol.11, issue.1, p.2636, 2015.
, Dynamics of Concentration in a Population Model Structured by Age and a Phenotypical Trait, Acta Applicandae Mathematicae, vol.11, issue.4, 2017.
DOI : 10.1051/mmnp/201611411
URL : https://hal.archives-ouvertes.fr/hal-01493068
, Manipulation and Motion of Organelles and Single Molecules in Living Cells, Chemical Reviews, vol.117, issue.5, p.43424375, 2017.
DOI : 10.1021/acs.chemrev.6b00638
, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, p.1249, 1988.
DOI : 10.1016/0021-9991(88)90002-2
URL : http://www.ann.jussieu.fr/~frey/papers/levelsets/Osher S., Fronts propagating with curvature dependent speed.pdf
, Self-averaging from lateral diversity in the itôschrödinger equation, Multiscale Modeling & Simulation, vol.6, issue.2, p.468492, 2007.
, The bacterial cytoplasm has glass-like properties and is uidized by metabolic activity, Cell, vol.156, issue.12, p.183194, 2014.
, Les atomes. Félix Alcan, 1913.
, Parabolic Equations in Biology: Growth, reaction, movement and diusion (Lecture Notes on Mathematical Modelling in the Life Sciences, 2015.
, Fractional Dierential Equations: An Introduction to Fractional Derivatives , Fractional Dierential Equations, Methods of Their Solution and Some ... (Mathematics in Science and Engineering, 1998.
, Classical and quantum transport in random media, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.6
DOI : 10.1016/S0021-7824(03)00038-2
URL : https://doi.org/10.1016/s0021-7824(03)00038-2
, Anomalous Transport: Foundations and Applications, 2008.
, Hyperbolic Partial Dierential Equations and Geometric Optics, Graduate Studies in Mathematics, 2012.
DOI : 10.1090/gsm/133
, Einstein's invention of Brownian motion, Annalen der Physik, vol.1, issue.S1, p.2337, 2005.
DOI : 10.1002/bbpc.19060125102
, Superdiusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic acanthamoeba castellanii Article, p.11690, 2015.
, Atmospheric diusion shown on a distance-neighbour graph, Containing Papers of a Mathematical and Physical Character, p.709737, 1926.
, A Biological Interpretation of Transient Anomalous Subdiusion. I. Qualitative Model, Biophysical Journal, vol.92, issue.4, p.11781191, 2007.
, Single Particle Tracking, Biophysical Journal, vol.72, issue.4, p.17441753, 1997.
DOI : 10.1007/978-1-59745-397-4_6
, Anomalous transit-time dispersion in amorphous solids, Physical Review B, vol.177, issue.10, p.24552477, 1975.
DOI : 10.1103/PhysRev.177.1182
, Front propagation in a one-dimensional autocatalytic reaction-subdiusion system, Physical Review E, vol.79, issue.4, 2009.
, Fluorescence correlation spectroscopy with single-molecule sensitivity on cell and model membranes, Cytometry, vol.4, issue.3, p.176182, 1999.
DOI : 10.1002/1361-6374(199609)4:3<149::AID-BIO5>3.3.CO;2-4
URL : http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0320(19990701)36:3<176::AID-CYTO5>3.0.CO;2-F/pdf
, Asymptotic solutions of continuous-time random walks, Journal of Statistical Physics, vol.10, issue.5, p.421434, 1974.
, Ecient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys, vol.77, issue.2, p.439471, 1988.
, Ecient implementation of essentially nonoscillatory shock-capturing schemes. II, J. Comput. Phys, vol.83, issue.1, p.3278, 1989.
, Lévy ights from a continuous-time process, Physical Review E, vol.63, issue.1, 2000.
, Anomalous versus slowed-down brownian diusion in the ligand-binding equilibrium, Biophysical Journal, vol.105, issue.9, p.20642073, 2013.
, The solution to subdiusion-reaction equation for the system with one mobile and one static reactant, Acta Physica Polonica B, issue.5, p.2013
, Quantitative Analysis of Single Particle Trajectories: Mean Maximal Excursion Method, Biophysical Journal, vol.98, issue.7, p.9813641372, 2010.
DOI : 10.1016/j.bpj.2009.12.4282
, Error rates in the Darling???Kac law, Studia Mathematica, vol.220, issue.2, p.101117, 2014.
DOI : 10.4064/sm220-2-1
, Retrograde semaphorin signaling regulates synapse elimination in the developing mouse brain, Science, vol.36, issue.7, p.34410201023, 2014.
DOI : 10.1111/j.1460-9568.2012.08203.x
, On generalized Csiszár-Kullback inequalities, Monatsh. Math, vol.131, issue.3, p.235253, 2000.
DOI : 10.1007/s006050070013
, Large deviations. The Annals of Probability, p.397419, 2008.
, Morphogenetic action through ux-limited spreading, Physics of Life Reviews, vol.10, issue.4, p.457475, 2013.
DOI : 10.1016/j.plrev.2013.06.004
, Méthodes Level Set pour des problèmes d'interface en microuidique, 2007.
, Topics in Optimal Transportation, Graduate Studies in Mathematics, vol.58, 2003.
DOI : 10.1090/gsm/058
, Systematic derivation of reaction-diusion equations with distributed delays and relations to fractional reaction-diusion equations and hyperbolic transport equations: Application to the theory of neolithic transition, Physical Review E, issue.6, p.66, 2002.
, Fronts in anomalous diffusion-reaction systems, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.6, issue.5, p.20120179, 1982.
DOI : 10.1209/0295-5075/82/58003
URL : http://rsta.royalsocietypublishing.org/content/roypta/371/1982/20120179.full.pdf
, Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen, Annalen der Physik, vol.1, issue.14, p.756780, 1906.
DOI : 10.1002/recl.19000190703
, Eine verallgemeinerung der quantenbedingungen für die zwecke der wellenmechanik . Zeitschrift für Physik, p.518529, 1926.
DOI : 10.1007/bf01397171
, Composition of isolated synaptic boutons reveals the amounts of vesicle tracking proteins, Science, issue.6187, p.34410231028, 2014.
, STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis, Nature, issue.7086, p.440935939, 2006.
, Propagating fronts in reactiontransport systems with memory, Physics Letters A, vol.371, pp.5-6374378, 2007.
, Kinetic equations for reaction-subdiusion systems: Derivation and stability analysis, Physical Review E, vol.74, issue.6, 2006.
DOI : 10.1103/physreve.74.066118
, Application of fractional calculus to reactionsubdiusion processes and morphogen gradient formation, 2014.
, Reaction-subdiusion model of morphogen gradient formation, Physical Review E, vol.82, issue.6, 2010.
, Anomalous Transport , chapter Subdiusion-Limited Reactions, 2008.
, From Becker-D??ring to Lifshitz-Slyozov: deriving the non-local boundary condition of a non-linear transport equation, ITM Web of Conferences, vol.137, p.17, 2015.
DOI : 10.1063/1.4772598
, Basic Theory of Fractional Dierential Equations, World Scientic Publishing Company, 2014.
, nous étudions la décroissance auto-similaire de la solution d'une équation de renouvellement à queue lourde vers un état stationnaire
, Nous y prouvons un résultat de stabilité : les solutions des problèmes rééchelonnés à ? > 0 convergent lorsque ? ? 0 vers la solution de viscosité de l'équation de Hamilton-Jacobi limite des problèmes à ? > 0
, des simulations numériques de type Monte Carlo, schémas volumes nis, Lax-Friedrichs et Weighted Essentially Non Oscillating ont été réalisées
, Analyse asymptotique, équations aux dérivées partielles, diusion anormale, équations structurées, entropie relative, équations de Hamilton-Jacobi, sous-diusion en biologie cel- lulaire