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Controllability of fast diffusion coupled parabolic systems
| 1. | BCAM - Basque Center for Applied Mathematics, Mazarredo 14, E-48009 Bilbao, Basque Country, Spain |
| 2. | Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris 6, Boîte Corrier 187, F-75252, Paris Cedex 05, France |
| 3. | Laboratoire de Mathématiques de Versailles, Université de Versailles - St. Quentin, 45 Avenue des Etats Unis, 78035 Versailles |
References:
| [1] |
F. Ammar-Khodja, A. Benabdallah and C. Dupaix, Null controllability of some reaction-diffusion systems with one control force, J. Math. Anal. Appl., 320 (2006), 928-943.
doi: 10.1016/j.jmaa.2005.07.060. |
| [2] |
M. Bendahmane and F. W. Chaves-Silva, Uniform null controllability for a degenerating reaction-diffusion system approximating a simplified cardiac model,, preprint, ().
|
| [3] |
J.-M. Coron and S. Guerrero, A singular optimal control: A linear 1-D parabolic hyperbolic example, Asymptot. Analisys, 44 (2005), 237-257. |
| [4] |
E. Fernandéz-Cara, J. Limaco and S. B. de Menezes, Null controllability for a parabolic-elliptic coupled system, Bull. Braz. Math. Soc. (N.S.), 44 (2013), 285-308.
doi: 10.1007/s00574-013-0014-x. |
| [5] |
A. V. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series 34, Research Institute of Mathematics, Seoul National University, Seoul, 1996. |
| [6] |
O. Glass, A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit, J. Funct. Analysis, 258 (2010), 852-868.
doi: 10.1016/j.jfa.2009.06.035. |
| [7] |
M. González-Burgos and R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force, Asymptot. Anal., 46 (2006), 123-162. |
| [8] |
S. Guerrero, Null controllability of some systems of two parabolic equations with one control force, SIAM J. Control Optim., 46 (2007), 379-394.
doi: 10.1137/060653135. |
| [9] |
S. Guerrero and G. Lebeau, Singular optimal control for a transport-diffusion equation, Comm. Partial Differential Equations, 32 (2007), 1813-1836.
doi: 10.1080/03605300701743756. |
| [10] |
D. Horstmann, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, I, Jahresber. Dtsch. Math.-Ver, 105 (2003), 103-165. |
| [11] |
A. Lopes, X. Zhang and E. Zuazua, Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations, J. Math. Pures Appl., 79 (2000), 741-808.
doi: 10.1016/S0021-7824(99)00144-0. |
| [12] |
J.-L. Lions, Some Methods in Mathematical Analysis of System and their Control, Science Press, Beijing, China, Gordon and Breach, New York, 1981. |
| [13] |
J.-L. Lions and E. Magenes, Problèmes aux Limites Non Homogènes et Applications, volumes 1, 2 et 3, Dunod, Paris, 1968. |
show all references
References:
| [1] |
F. Ammar-Khodja, A. Benabdallah and C. Dupaix, Null controllability of some reaction-diffusion systems with one control force, J. Math. Anal. Appl., 320 (2006), 928-943.
doi: 10.1016/j.jmaa.2005.07.060. |
| [2] |
M. Bendahmane and F. W. Chaves-Silva, Uniform null controllability for a degenerating reaction-diffusion system approximating a simplified cardiac model,, preprint, ().
|
| [3] |
J.-M. Coron and S. Guerrero, A singular optimal control: A linear 1-D parabolic hyperbolic example, Asymptot. Analisys, 44 (2005), 237-257. |
| [4] |
E. Fernandéz-Cara, J. Limaco and S. B. de Menezes, Null controllability for a parabolic-elliptic coupled system, Bull. Braz. Math. Soc. (N.S.), 44 (2013), 285-308.
doi: 10.1007/s00574-013-0014-x. |
| [5] |
A. V. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series 34, Research Institute of Mathematics, Seoul National University, Seoul, 1996. |
| [6] |
O. Glass, A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit, J. Funct. Analysis, 258 (2010), 852-868.
doi: 10.1016/j.jfa.2009.06.035. |
| [7] |
M. González-Burgos and R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force, Asymptot. Anal., 46 (2006), 123-162. |
| [8] |
S. Guerrero, Null controllability of some systems of two parabolic equations with one control force, SIAM J. Control Optim., 46 (2007), 379-394.
doi: 10.1137/060653135. |
| [9] |
S. Guerrero and G. Lebeau, Singular optimal control for a transport-diffusion equation, Comm. Partial Differential Equations, 32 (2007), 1813-1836.
doi: 10.1080/03605300701743756. |
| [10] |
D. Horstmann, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, I, Jahresber. Dtsch. Math.-Ver, 105 (2003), 103-165. |
| [11] |
A. Lopes, X. Zhang and E. Zuazua, Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations, J. Math. Pures Appl., 79 (2000), 741-808.
doi: 10.1016/S0021-7824(99)00144-0. |
| [12] |
J.-L. Lions, Some Methods in Mathematical Analysis of System and their Control, Science Press, Beijing, China, Gordon and Breach, New York, 1981. |
| [13] |
J.-L. Lions and E. Magenes, Problèmes aux Limites Non Homogènes et Applications, volumes 1, 2 et 3, Dunod, Paris, 1968. |
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