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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.
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, (). Google Scholar |
[3] |
J.-M. Coron and S. Guerrero, A singular optimal control: A linear 1-D parabolic hyperbolic example,, Asymptot. Analisys, 44 (2005), 237.
|
[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.
doi: 10.1007/s00574-013-0014-x. |
[5] |
A. V. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations,, Lecture Notes Series 34, (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.
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.
|
[8] |
S. Guerrero, Null controllability of some systems of two parabolic equations with one control force,, SIAM J. Control Optim., 46 (2007), 379.
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.
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.
|
[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.
doi: 10.1016/S0021-7824(99)00144-0. |
[12] |
J.-L. Lions, Some Methods in Mathematical Analysis of System and their Control,, Science Press, (1981).
|
[13] |
J.-L. Lions and E. Magenes, Problèmes aux Limites Non Homogènes et Applications,, volumes 1, (1968). Google Scholar |
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.
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, (). Google Scholar |
[3] |
J.-M. Coron and S. Guerrero, A singular optimal control: A linear 1-D parabolic hyperbolic example,, Asymptot. Analisys, 44 (2005), 237.
|
[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.
doi: 10.1007/s00574-013-0014-x. |
[5] |
A. V. Fursikov and O. Yu. Imanuvilov, Controllability of Evolution Equations,, Lecture Notes Series 34, (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.
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.
|
[8] |
S. Guerrero, Null controllability of some systems of two parabolic equations with one control force,, SIAM J. Control Optim., 46 (2007), 379.
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.
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.
|
[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.
doi: 10.1016/S0021-7824(99)00144-0. |
[12] |
J.-L. Lions, Some Methods in Mathematical Analysis of System and their Control,, Science Press, (1981).
|
[13] |
J.-L. Lions and E. Magenes, Problèmes aux Limites Non Homogènes et Applications,, volumes 1, (1968). Google Scholar |
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