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Long-time behavior for a class of degenerate parabolic equations
Generalized exact boundary synchronization for a coupled system of wave equations
| 1. | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
| 2. | Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg |
| 3. | School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai 200433 |
References:
| [1] |
A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, 2nd Edition, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer-Verlag, New York, 2003. |
| [2] |
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd Edition, Cambridge University Press, Cambridge, 2013. |
| [3] |
Long Hu, Fanqiong Ji and Ke Wang, Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations, Chin. Ann. Math. Ser. B, 34 (2013), 479-490.
doi: 10.1007/s11401-013-0785-9. |
| [4] |
Long Hu, Tatsien Li and Bopeng Rao, Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type, Communications on Pure and Applied Analysis, 13 (2014). DOI: 10.3934/cpaa.2014.13 |
| [5] |
Tatsien Li, Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Series on Applied Mathematics, 3, American Institute of Mathematical Sciences (AIMS), Springfield, MO; Higher Education Press, Beijing, 2010. |
| [6] |
Tatsien Li and Bopeng Rao, Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chin. Ann. Math. Ser. B, 31 (2010), 723-742.
doi: 10.1007/s11401-010-0600-9. |
| [7] |
Tatsien Li and Bopeng Rao, Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls, Chin. Ann. Math. Ser. B, 34 (2013), 139-160.
doi: 10.1007/s11401-012-0754-8. |
| [8] |
Tatsien Li and Bopeng Rao, A note on the exact synchronization by groups for a coupled system of wave equations,, to appear in Math. Meth. Appl. Sci., ().
|
| [9] |
Tatsien Li, Bopeng Rao and Long Hu, Exact boundary synchronization for a coupled system of 1-D wave equations,, to appear in ESAIM: COCV. DOI: 10.1051/COCV/2013066, ().
|
| [10] |
J.-L. Lions, Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués, Vol. 1, Masson, 1988. |
| [11] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Review, 30 (1988), 1-68.
doi: 10.1137/1030001. |
| [12] |
D. L. Russell, Controllability and stabilization theory for linear partial differential equations: Recent progress and open questions, SIAM Review, 20 (1978), 639-739.
doi: 10.1137/1020095. |
show all references
References:
| [1] |
A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, 2nd Edition, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer-Verlag, New York, 2003. |
| [2] |
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd Edition, Cambridge University Press, Cambridge, 2013. |
| [3] |
Long Hu, Fanqiong Ji and Ke Wang, Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations, Chin. Ann. Math. Ser. B, 34 (2013), 479-490.
doi: 10.1007/s11401-013-0785-9. |
| [4] |
Long Hu, Tatsien Li and Bopeng Rao, Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type, Communications on Pure and Applied Analysis, 13 (2014). DOI: 10.3934/cpaa.2014.13 |
| [5] |
Tatsien Li, Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Series on Applied Mathematics, 3, American Institute of Mathematical Sciences (AIMS), Springfield, MO; Higher Education Press, Beijing, 2010. |
| [6] |
Tatsien Li and Bopeng Rao, Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chin. Ann. Math. Ser. B, 31 (2010), 723-742.
doi: 10.1007/s11401-010-0600-9. |
| [7] |
Tatsien Li and Bopeng Rao, Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls, Chin. Ann. Math. Ser. B, 34 (2013), 139-160.
doi: 10.1007/s11401-012-0754-8. |
| [8] |
Tatsien Li and Bopeng Rao, A note on the exact synchronization by groups for a coupled system of wave equations,, to appear in Math. Meth. Appl. Sci., ().
|
| [9] |
Tatsien Li, Bopeng Rao and Long Hu, Exact boundary synchronization for a coupled system of 1-D wave equations,, to appear in ESAIM: COCV. DOI: 10.1051/COCV/2013066, ().
|
| [10] |
J.-L. Lions, Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués, Vol. 1, Masson, 1988. |
| [11] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Review, 30 (1988), 1-68.
doi: 10.1137/1030001. |
| [12] |
D. L. Russell, Controllability and stabilization theory for linear partial differential equations: Recent progress and open questions, SIAM Review, 20 (1978), 639-739.
doi: 10.1137/1020095. |
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