, Controllability results for some nonlinear coupled parabolic systems by one control force
, Controllability results for cascade systems of m coupled parabolic PDEs by one control force, In : Port. Math, vol.671, issue.108, pp.91-113, 2010.
, Remarks on non controllability of the heat equation with memory, In : ESAIM Control Optim. Calc. Var, vol.191, issue.20, pp.288-300, 2013.
, Partial differential relations. T. 9, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas, pp.363-73, 1986.
, Controllability of systems of Stokes equations with one control force: existence of insensitizing controls, Non Linéaire, vol.246, pp.1029-1054, 2007.
, Null controllability of some systems of two parabolic equations with one control force, In : SIAM J. Control Optim, vol.462, issue.100, pp.379-394, 2007.
, A user's guide to PDE models for chemotaxis, J. Math. Biol, vol.581, issue.2 1, pp.183-217, 2009.
, Topics in mathematical system theory, pp.358-368, 1969.
, Unique continuation principle for systems of parabolic equations, In : ESAIM Control Optim. Calc. Var, vol.162, issue.101, pp.247-274, 2010.
, Effects of cell motility and chemotaxis on microbial population growth, In : Biophysical journal, vol.403, issue.1, p.209, 1982.
, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles Avant propos de P. Lelong. Paris : Dunod, pp.426-98, 1968.
, Sur la contrôlabilité et son coût pour quelques équations aux dérivées partielles, p.29, 2013.
, Contrôle exact de l'équation de la chaleur, In : Comm. Partial Differential Equations, vol.201, issue.2, pp.335-356, 1995.
, Linear and quasilinear equations of parabolic type, In : Translated from the Russian by S. Smith. Translations of Mathematical Monographs, vol.23, pp.648-677, 1968.
, The control transmutation method and the cost of fast controls, In : SIAM J. Control Optim, vol.452, pp.762-772, 2006.
, Controllability to trajectories for some parabolic systems of three and two equations by one control force, In : Math. Control Relat. Fields, vol.41, issue.100, pp.17-44, 2014.
, Null controllability of the N-dimensional Stokes system with N ´ 1 scalar controls, J. Differential Equations, vol.2467, pp.2908-2921, 2009.
, Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components, In : Invent. Math, vol.1983, issue.90, pp.833-880, 2014.
, Partial differential equations. Second. T. 19. Graduate Studies in Mathematics, pp.67-78, 2010.
, Null controllability of the heat equation with boundary Fourier conditions: the linear case, In : ESAIM Control Optim. Calc. Var, vol.123, pp.442-465, 2006.
, Controllability of evolution equations, pp.76-134, 1996.
, Controllability results for some nonlinear coupled parabolic systems by one control force, In : Asymptot. Anal, vol.46, issue.16, pp.123-162, 0193.
, Controllability results for cascade systems of m coupled parabolic PDEs by one control force, In : Port. Math, vol.671, issue.108, pp.91-113, 2010.
, Partial differential relations. T. 9, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas, pp.363-73, 1986.
, Null controllability of some systems of two parabolic equations with one control force, In : SIAM J. Control Optim, vol.462, issue.100, pp.379-394, 2007.
, Indirect controllability of locally coupled systems under geometric conditions, Comptes Rendus Mathematique, vol.3497, pp.395-400, 2011.
, Indirect controllability of locally coupled wave-type systems and applications, In : J. Math. Pures Appl, vol.99, pp.544-576, 2013.
, Null-controllability of some systems of parabolic type by one control force, In : ESAIM Control Optim. Calc. Var, vol.113, pp.426-448, 2005.
, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, In : Differ. Equ. Appl, vol.1, issue.55, pp.427-457, 2009.
, A Kalman rank condition for the localized distributed controllability of a class of linear parbolic systems, In : J. Evol. Equ, vol.92, issue.37, pp.267-291, 2009.
, Recent results on the controllability of linear coupled parabolic problems: a survey, In : Math. Control Relat. Fields, vol.13, issue.135, pp.267-306, 2011.
, Controllability of some system of parabolic equations, Procedings of the II Encuentro RSME-SMM. 2012 (cf, p.99
, Minimal time of controllability of two parabolic equations with disjoint control and coupling domains, Math. Acad
, New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence, pp.120-124
, Controllability to trajectories for some parabolic systems of three and two equations by one control force, In : Math. Control Relat. Fields, vol.41, issue.100, pp.17-44, 2014.
, Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients, In : Math. Control Relat. Fields, vol.43, issue.101, pp.263-287, 2014.
, Controllability of two coupled wave equations on a compact manifold, Arch. Rational Mech. Anal, vol.211, pp.113-187, 2014.
, Indirect controllability of some linear parabolic systems of m equations with m -1 controls involving coupling terms of zero or first order, In : Submitted, vol.29, issue.100, pp.33-125, 2015.
, Some remarks on complete controllability, In : SIAM J. Control, vol.4, issue.100, pp.686-694, 1966.
, Boundary controllability of parabolic coupled equations, In : J. Funct. Anal, vol.2597, issue.107, pp.1720-1758, 2010.
, Controllability results for cascade systems of m coupled parabolic PDEs by one control force, In : Port. Math, vol.671, issue.108, pp.91-113, 2010.
, Null controllability of some systems of two parabolic equations with one control force, In : SIAM J. Control Optim, vol.462, issue.100, pp.379-394, 2007.
, Unique continuation principle for systems of parabolic equations, In : ESAIM Control Optim. Calc. Var, vol.162, issue.101, pp.247-274, 2010.
, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles Avant propos de P. Lelong. Paris : Dunod, pp.426-98, 1968.
, The control transmutation method and the cost of fast controls, In : SIAM J. Control Optim, vol.452, pp.762-772, 2006.
, Boundary approximate controllability of some linear parabolic systems, In : Evol. Equ. Control Theory, vol.31, issue.101, pp.167-189, 2014.
, Exact controllability of a cascade system of conservative equations, C. R. Math. Acad. Sci. Paris, vol.349, pp.5-6, 2011.
, System (5.1) is ? 1 -approximately controllable and we observe indeed in Figure A.1 and A.2 that the norm of the numerical solution to System (5.1) at time T (´´) is decreasing when reducing the penality parameter ? = h 4 A hierarchic multi-level energy method for the control of bidiagonal and mixed n-coupled cascade systems of PDE's by a reduced number of controls, As mentioned in the introduction of the present article Figure A.1, the minimal value of the functional F h,?t References, pp.11-12, 2013.
, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, In : Differ. Equ. Appl, vol.1, issue.55, pp.427-457, 2009.
, A Kalman rank condition for the localized distributed controllability of a class of linear parbolic systems, In : J. Evol. Equ, vol.92, issue.37, pp.267-291, 2009.
, Recent results on the controllability of linear coupled parabolic problems: a survey, In : Math. Control Relat. Fields, vol.13, issue.135, pp.267-306, 2011.
, Minimal time of controllability of two parabolic equations with disjoint control and coupling domains, Math. Acad
, New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence, pp.120-124
, Controllability to trajectories for some parabolic systems of three and two equations by one control force, In : Math. Control Relat. Fields, vol.41, issue.100, pp.17-44, 2014.
, Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients, In : Math. Control Relat. Fields, vol.43, issue.101, pp.263-287, 2014.
, On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems, CANUM 2012, 41e Congrès National d'Analyse Numérique. T. 41. ESAIM Proc. EDP Sci., Les Ulis, pp.15-58, 2013.
, Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method, Math. biosci, vol.219, issue.2, pp.129-141, 2009.
, Analyse convexe et problèmes variationnels Dunod; Gauthier-Villars, Collection Études Mathématiques, vol.170, pp.340-158, 1974.
, Boundary controllability of parabolic coupled equations, In : J. Funct. Anal, vol.2597, issue.107, pp.1720-1758, 2010.
, The cost of approximate controllability for heat equations: the linear case, In : Adv. Differential Equations, vol.5, pp.4-6, 2000.
, Controllability of evolution equations, pp.76-134, 1996.
, Exact controllability theorems for linear parabolic equations in one space dimension, In : Arch. Rational Mech. Anal, vol.43, pp.272-292, 1971.
, Controllability results for cascade systems of m coupled parabolic PDEs by one control force, In : Port. Math, vol.671, issue.108, pp.91-113, 2010.
, Some backward uniqueness results, In : Nonlinear Anal, vol.108, pp.777-790, 1986.
, Remarks on non controllability of the heat equation with memory, In : ESAIM Control Optim. Calc. Var, vol.191, issue.20, pp.288-300, 2013.
, Exact and approximate controllability for distributed parameter systems. T. 117. Encyclopedia of Mathematics and its Applications, pp.458-165, 2008.
, Problèmes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, pp.251-94, 1968.
, On the null controllability of a 3 x 3 parabolic system with non-constant coefficients by one or two control forces, In : J. Math. Pures Appl, vol.992, issue.9, pp.187-210, 2013.
, Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques, In : Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math, vol.31, pp.219-239, 1958.
, Null-controllability for some linear parabolic systems with controls acting on different parts of the domain and its boundary, Math. Control Signals Systems, pp.257-280, 2012.
, = p1´?qp1´?qzp1´p1´?qp1p1´?qp1´p1´?qp1´?qz est solution du système $ ' ' ' ' & ' ' ' ' % References, Contrôlabilité et contrôle optimal References w Numerical linear algebra. T. 55. Texts in Applied Mathematics. Translated from the 2002 French original by Karim Trabelsi, pp.271-181, 2008.
, Partial null controllability of parabolic linear systems by m forces, pp.2015-54
, Analyse numérique et optimisation: une introduction à la modélisation mathématique et à la simulation numérique, Editions Ecole Polytechnique, pp.174-181, 2005.
, Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity, Comm. Partial Differential Equations, vol.29, issue.16, pp.7-8, 2004.
, Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient, In : Nonlinear Anal, vol.57, issue.24, pp.5-6, 2004.
, Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations, In : J. Math. Pures Appl, vol.933, issue.175, pp.240-276, 2010.
, Discrete Carleman estimates for elliptic operators in arbitrary dimension and applications, In : SIAM J. Control Optim, vol.488, issue.175, pp.5357-5397, 2010.
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, On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems, CANUM 2012, 41e Congrès National d'Analyse Numérique. T. 41. ESAIM Proc. EDP Sci., Les Ulis, pp.15-58, 2013.
, Introduction à l'analyse numérique matricielle et à l'optimisation. Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], pp.279-168, 1982.
, Analyse mathématique et calcul numérique pour les sciences et les techniques INSTN: Collection Enseignement. [INSTN: Teaching Collection]. Évolution: semi-groupe, variationnel. [Evolution: semigroups , variational methods], Reprint of the 1985 edition, pp.345-854, 1988.
, Analyse convexe et problèmes variationnels Dunod; Gauthier-Villars, Collection Études Mathématiques, vol.170, pp.340-158, 1974.
, Convex cones, sets, and functions, p.170, 1953.
, Numerical null controllability of a semilinear heat equation via a least squares method, C. R. Math. Acad. Sci. Paris, vol.349, pp.15-16, 2011.
, Numerical null controllability of semilinear 1-D heat equations: fixed point, least squares and Newton methods, In : Math. Control Relat. Fields, vol.23, pp.217-246, 2012.
, Strong convergent approximations of null controls for the 1D heat equation, pp.49-78, 2013.
, Numerical exact controllability of the 1D heat equation: duality and Carleman weights, In : J. Optim. Theory Appl, vol.1631, pp.253-285, 2014.
, On conjugate convex functions, In : Canadian J. Math, vol.1, pp.73-77, 1949.
, Controllability of evolution equations, pp.76-134, 1996.
, Optimal control of distributed systems: theory and applications. T. 187, p.170, 2000.
, Controllability results for some nonlinear coupled parabolic systems by one control force, In : Asymptot. Anal, vol.46, issue.16, pp.123-162, 0193.
, Exact and approximate controllability for distributed parameter systems. T. 117. Encyclopedia of Mathematics and its Applications, pp.458-165, 2008.
, SciPy: Open source scientific tools for Python. [Online; accessed 2015-09-16, p.2001
, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles Avant propos de P. Lelong. Paris : Dunod, pp.426-98, 1968.
, Uniform controllability of semidiscrete approximations of parabolic control systems, Systems Control Lett, vol.557, issue.175, pp.597-609, 2006.
, DOLFIN: Automated Finite Element Computing, In : ACM Transactions on Mathematical Software, vol.372, issue.187, 2010.
, Semigroups of linear operators and applications to partial differential equations . T. 44 Applied Mathematical Sciences, pp.279-282, 1983.
, Extension of Fenchel's duality theorem for convex functions, In : Duke Math. J, vol.33, pp.81-89, 1966.
, A hierarchic multi-level energy method for the control of bidiagonal and mixed n-coupled cascade systems of PDE's by a reduced number of controls, In : Adv. Differential Equations, vol.18, issue.36, pp.11-12, 2013.
, Internal controllability of first order quasilinear hyperbolic systems with a reduced number of controls, pp.29-73, 2015.
, Indirect controllability of locally coupled systems under geometric conditions, Comptes Rendus Mathematique, vol.3497, pp.395-400, 2011.
, Indirect controllability of locally coupled wave-type systems and applications, In : J. Math. Pures Appl, vol.995, issue.9, pp.544-576, 2013.
, Indirect controllability of locally coupled wave-type systems and applications, In : J. Math. Pures Appl, vol.99, pp.544-576, 2013.
, Controllability to the trajectories of phase-field models by one control force, In : SIAM J. Control Optim, vol.425, pp.1661-1680, 2003.
, Null-controllability of some systems of parabolic type by one control force, In : ESAIM Control Optim. Calc. Var, vol.113, pp.426-448, 2005.
, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems, In : Differ. Equ. Appl, vol.1, issue.55, pp.427-457, 2009.
, A Kalman rank condition for the localized distributed controllability of a class of linear parbolic systems, In : J. Evol. Equ, vol.92, issue.37, pp.267-291, 2009.
, The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials, J. Math. Pures Appl, vol.966, issue.9, pp.555-590, 2011.
, Controllability of some system of parabolic equations, Procedings of the II Encuentro RSME-SMM. 2012 (cf, p.99
, Minimal time of controllability of two parabolic equations with disjoint control and coupling domains, Math. Acad
, New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence, pp.120-124
, Numerical linear algebra. T. 55. Texts in Applied Mathematics. Translated from the, pp.271-181, 2002.
, Null-controllability of some reaction-diffusion systems with one control force, J. Math. Anal. Appl, vol.320, issue.2, pp.928-943, 2006.
, Null-controllability of some reaction-diffusion systems with one control force, J. Math. Anal. Appl, vol.320, issue.2, pp.928-943, 2006.
, Partial null controllability of parabolic linear systems by m forces, pp.2015-54
, Analyse numérique et optimisation: une introduction à la modélisation mathématique et à la simulation numérique, Editions Ecole Polytechnique, pp.174-181, 2005.
, Controllability to trajectories for some parabolic systems of three and two equations by one control force, In : Math. Control Relat. Fields, vol.41, issue.100, pp.17-44, 2014.
, A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions, In : SIAM J. Control Optim, vol.433, issue.24, pp.955-969, 2004.
, Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity, Comm. Partial Differential Equations, vol.29, issue.16, pp.7-8, 2004.
, Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient, In : Nonlinear Anal, vol.57, issue.24, pp.5-6, 2004.
, A reaction-diffusion system with fast reversible reaction, J. Math. Anal. Appl, vol.2861, issue.1, pp.125-135, 2003.
, Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations, In : J. Math. Pures Appl, vol.933, issue.175, pp.240-276, 2010.
, Discrete Carleman estimates for elliptic operators in arbitrary dimension and applications, In : SIAM J. Control Optim, vol.488, issue.175, pp.5357-5397, 2010.
, Uniform controllability properties for space/time-discretized parabolic equations, In : Numer. Math, vol.1184, issue.175, pp.601-661, 2011.
, Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.315, issue.175, pp.1035-1078, 2014.
, Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients, In : Math. Control Relat. Fields, vol.43, issue.101, pp.263-287, 2014.
, On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems, CANUM 2012, 41e Congrès National d'Analyse Numérique. T. 41. ESAIM Proc. EDP Sci., Les Ulis, pp.15-58, 2013.
, Null controllability of the N-dimensional Stokes system with N ´ 1 scalar controls, J. Differential Equations, vol.2467, pp.2908-2921, 2009.
, Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method, Math. biosci, vol.219, issue.2, pp.129-141, 2009.
, Introduction à l'analyse numérique matricielle et à l'optimisation. Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], pp.279-168, 1982.
, Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components, In : Invent. Math, vol.1983, issue.90, pp.833-880, 2014.
, Controllability of two coupled wave equations on a compact manifold, Arch. Rational Mech. Anal, vol.211, pp.113-187, 2014.
, Indirect controllability of some linear parabolic systems of m equations with m -1 controls involving coupling terms of zero or first order, In : Submitted, vol.29, issue.100, pp.33-125, 2015.
, Analyse mathématique et calcul numérique pour les sciences et les techniques INSTN: Collection Enseignement. [INSTN: Teaching Collection]. Évolution: semi-groupe, variationnel. [Evolution: semigroups , variational methods], Reprint of the 1985 edition, pp.345-854, 1988.
, On the controllability of parabolic systems with a nonlinear term involving the state and the gradient, In : SIAM J. Control Optim, vol.413, pp.798-819, 2002.
, A general theory of observation and control, In : SIAM J. Control Optimization, vol.152, pp.185-220, 1977.
, Controllability of a 2X2 parabolic system by one force with space-dependent coupling term of order one, In : submited, 2015.
, Analyse convexe et problèmes variationnels Dunod; Gauthier-Villars, Collection Études Mathématiques, vol.170, pp.340-158, 1974.
, Partial differential equations. Second. T. 19. Graduate Studies in Mathematics, pp.67-78, 2010.
, Some remarks on complete controllability, In : SIAM J. Control, vol.4, issue.100, pp.686-694, 1966.
, Convex cones, sets, and functions, p.170, 1953.
, Null controllability of the heat equation with boundary Fourier conditions: the linear case, In : ESAIM Control Optim. Calc. Var, vol.123, pp.442-465, 2006.
, Boundary controllability of parabolic coupled equations, In : J. Funct. Anal, vol.2597, issue.107, pp.1720-1758, 2010.
, Numerical null controllability of a semilinear heat equation via a least squares method, C. R. Math. Acad. Sci. Paris, vol.349, pp.15-16, 2011.
, Numerical null controllability of semilinear 1-D heat equations: fixed point, least squares and Newton methods, In : Math. Control Relat. Fields, vol.23, pp.217-246, 2012.
, Strong convergent approximations of null controls for the 1D heat equation, pp.49-78, 2013.
, Numerical exact controllability of the 1D heat equation: duality and Carleman weights, In : J. Optim. Theory Appl, vol.1631, pp.253-285, 2014.
, The cost of approximate controllability for heat equations: the linear case, In : Adv. Differential Equations, vol.5, pp.4-6, 2000.
, On conjugate convex functions, In : Canadian J. Math, vol.1, pp.73-77, 1949.
, Controllability of evolution equations, pp.76-134, 1996.
, Exact controllability theorems for linear parabolic equations in one space dimension, In : Arch. Rational Mech. Anal, vol.43, pp.272-292, 1971.
, Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations, In : Quart. Appl. Math, vol.3275, issue.16, pp.45-69, 1974.
, Optimal control of distributed systems: theory and applications. T. 187, p.170, 2000.
, Controllability results for some nonlinear coupled parabolic systems by one control force, In : Asymptot. Anal, vol.46, issue.16, pp.123-162, 0193.
, Controllability results for cascade systems of m coupled parabolic PDEs by one control force, In : Port. Math, vol.671, issue.108, pp.91-113, 2010.
, Some backward uniqueness results, In : Nonlinear Anal, vol.108, pp.777-790, 1986.
, Remarks on non controllability of the heat equation with memory, In : ESAIM Control Optim. Calc. Var, vol.191, issue.20, pp.288-300, 2013.
, Exact and approximate controllability for distributed parameter systems. T. 117. Encyclopedia of Mathematics and its Applications, pp.458-165, 2008.
, Partial differential relations. T. 9, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas, pp.363-73, 1986.
, Controllability of systems of Stokes equations with one control force: existence of insensitizing controls, Non Linéaire, vol.246, pp.1029-1054, 2007.
, Null controllability of some systems of two parabolic equations with one control force, In : SIAM J. Control Optim, vol.462, issue.100, pp.379-394, 2007.
, A user's guide to PDE models for chemotaxis, J. Math. Biol, vol.581, issue.2 1, pp.183-217, 2009.
, Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, In : Publ. Res. Inst. Math. Sci, vol.39, issue.2, pp.227-274, 2003.
, SciPy: Open source scientific tools for Python. [Online; accessed 2015-09-16, p.2001
, Topics in mathematical system theory, pp.358-368, 1969.
, Unique continuation principle for systems of parabolic equations, In : ESAIM Control Optim. Calc. Var, vol.162, issue.101, pp.247-274, 2010.
, Effects of cell motility and chemotaxis on microbial population growth, In : Biophysical journal, vol.403, issue.1, p.209, 1982.
, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles Avant propos de P. Lelong. Paris : Dunod, pp.426-98, 1968.
, Sur la contrôlabilité et son coût pour quelques équations aux dérivées partielles, p.29, 2013.
, Problèmes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, pp.251-94, 1968.
, Contrôle exact de l'équation de la chaleur, In : Comm. Partial Differential Equations, vol.201, issue.2, pp.335-356, 1995.
, Linear and quasilinear equations of parabolic type, In : Translated from the Russian by S. Smith. Translations of Mathematical Monographs, vol.23, pp.648-677, 1968.
, Uniform controllability of semidiscrete approximations of parabolic control systems, Systems Control Lett, vol.557, issue.175, pp.597-609, 2006.
, DOLFIN: Automated Finite Element Computing, In : ACM Transactions on Mathematical Software, vol.372, issue.187, 2010.
, On the null controllability of a 3 x 3 parabolic system with non-constant coefficients by one or two control forces, In : J. Math. Pures Appl, vol.992, issue.9, pp.187-210, 2013.
, The control transmutation method and the cost of fast controls, In : SIAM J. Control Optim, vol.452, pp.762-772, 2006.
, Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques, In : Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math, vol.31, pp.219-239, 1958.
, Null-controllability for some linear parabolic systems with controls acting on different parts of the domain and its boundary, Math. Control Signals Systems, pp.257-280, 2012.
, Boundary approximate controllability of some linear parabolic systems, In : Evol. Equ. Control Theory, vol.31, issue.101, pp.167-189, 2014.
, Semigroups of linear operators and applications to partial differential equations . T. 44 Applied Mathematical Sciences, pp.279-282, 1983.
, Extension of Fenchel's duality theorem for convex functions, In : Duke Math. J, vol.33, pp.81-89, 1966.
, Exact controllability of a cascade system of conservative equations, C. R. Math. Acad. Sci. Paris, vol.349, pp.5-6, 2011.
, Exact controllability of a cascade system of conservative equations, C. R. Math. Acad. Sci. Paris, vol.349, pp.5-6, 2011.
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