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The global solvability of a sixth order Cahn-Hilliard type equation via the Bäcklund transformation
Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type
1. | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
2. | Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg |
References:
[1] |
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., 34B (2013), 479-490.
doi: 10.1007/s11401-013-0785-9. |
[2] |
Tatsien Li, "Controllability and Observability for Quasilinear Hyperbolic Systems," AIMS Series on Applied Mathematies, Vol. 3, AIMS & Higher Education Press, 2010. |
[3] |
Tatsien Li and Bopeng Rao, Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chin. Ann. Math., 31B (2010), 723-742.
doi: 10.1007/s11401-010-0600-9. |
[4] |
Tatsien Li and Bopeng Rao, Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls, Chin. Ann. Math., 34B (2013), 139-160.
doi: 10.1007/s11401-012-0754-8. |
[5] |
Tatsien Li, Bopeng Rao and Long Hu, Exact boundary synchronization for a coupled system of 1-D wave equations,, To appear in ESAIM:COCV., ().
|
[6] |
Tatsien Li and Lixin Yu, Exact boundary controllability for 1-D quasilinear wave equations, SIAM J. Control. Optim, 45 (2006), 1074-1083.
doi: 10.1137/S0363012903427300. |
[7] |
J.-L. Lions, "Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués," Vol. 1, Masson, 1988. |
[8] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., 30 (1988), 1-68.
doi: 10.1137/1030001. |
[9] |
D. L. Russell, Controllability and stabilization theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), 639-739.
doi: 10.1137/1020095. |
[10] |
Ke Wang, Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems, Chin. Ann. Math., 32B (2011), 803-822.
doi: 10.1007/s11401-011-0683-y. |
[11] |
Lixin Yu, Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems and its applications, Math. Meth. Appl. Sci., 33 (2010), 273-286.
doi: 10.1002/mma.1167. |
show all references
References:
[1] |
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., 34B (2013), 479-490.
doi: 10.1007/s11401-013-0785-9. |
[2] |
Tatsien Li, "Controllability and Observability for Quasilinear Hyperbolic Systems," AIMS Series on Applied Mathematies, Vol. 3, AIMS & Higher Education Press, 2010. |
[3] |
Tatsien Li and Bopeng Rao, Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chin. Ann. Math., 31B (2010), 723-742.
doi: 10.1007/s11401-010-0600-9. |
[4] |
Tatsien Li and Bopeng Rao, Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls, Chin. Ann. Math., 34B (2013), 139-160.
doi: 10.1007/s11401-012-0754-8. |
[5] |
Tatsien Li, Bopeng Rao and Long Hu, Exact boundary synchronization for a coupled system of 1-D wave equations,, To appear in ESAIM:COCV., ().
|
[6] |
Tatsien Li and Lixin Yu, Exact boundary controllability for 1-D quasilinear wave equations, SIAM J. Control. Optim, 45 (2006), 1074-1083.
doi: 10.1137/S0363012903427300. |
[7] |
J.-L. Lions, "Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués," Vol. 1, Masson, 1988. |
[8] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., 30 (1988), 1-68.
doi: 10.1137/1030001. |
[9] |
D. L. Russell, Controllability and stabilization theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), 639-739.
doi: 10.1137/1020095. |
[10] |
Ke Wang, Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems, Chin. Ann. Math., 32B (2011), 803-822.
doi: 10.1007/s11401-011-0683-y. |
[11] |
Lixin Yu, Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems and its applications, Math. Meth. Appl. Sci., 33 (2010), 273-286.
doi: 10.1002/mma.1167. |
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