-
Previous Article
Hodge-de Rham theory on fractal graphs and fractals
- CPAA Home
- This Issue
-
Next Article
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.
doi: 10.1007/s11401-013-0785-9. |
[2] |
Tatsien Li, "Controllability and Observability for Quasilinear Hyperbolic Systems,", AIMS Series on Applied Mathematies, (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.
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.
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., (). Google Scholar |
[6] |
Tatsien Li and Lixin Yu, Exact boundary controllability for 1-D quasilinear wave equations,, SIAM J. Control. Optim, 45 (2006), 1074.
doi: 10.1137/S0363012903427300. |
[7] |
J.-L. Lions, "Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués,", Vol. 1, (1988). Google Scholar |
[8] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems,, SIAM Rev., 30 (1988), 1.
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.
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.
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.
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.
doi: 10.1007/s11401-013-0785-9. |
[2] |
Tatsien Li, "Controllability and Observability for Quasilinear Hyperbolic Systems,", AIMS Series on Applied Mathematies, (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.
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.
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., (). Google Scholar |
[6] |
Tatsien Li and Lixin Yu, Exact boundary controllability for 1-D quasilinear wave equations,, SIAM J. Control. Optim, 45 (2006), 1074.
doi: 10.1137/S0363012903427300. |
[7] |
J.-L. Lions, "Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués,", Vol. 1, (1988). Google Scholar |
[8] |
J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems,, SIAM Rev., 30 (1988), 1.
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.
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.
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.
doi: 10.1002/mma.1167. |
[1] |
Olena Naboka. On synchronization of oscillations of two coupled Berger plates with nonlinear interior damping. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1933-1956. doi: 10.3934/cpaa.2009.8.1933 |
[2] |
Gelasio Salaza, Edgardo Ugalde, Jesús Urías. Master--slave synchronization of affine cellular automaton pairs. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 491-502. doi: 10.3934/dcds.2005.13.491 |
[3] |
Valery Y. Glizer. Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay. Numerical Algebra, Control & Optimization, 2020 doi: 10.3934/naco.2020027 |
[4] |
Michael Schmidt, Emmanuel Trélat. Controllability of couette flows. Communications on Pure & Applied Analysis, 2006, 5 (1) : 201-211. doi: 10.3934/cpaa.2006.5.201 |
[5] |
Jean-François Biasse. Improvements in the computation of ideal class groups of imaginary quadratic number fields. Advances in Mathematics of Communications, 2010, 4 (2) : 141-154. doi: 10.3934/amc.2010.4.141 |
[6] |
Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations & Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379 |
[7] |
Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 |
[8] |
Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 |
[9] |
Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027 |
[10] |
Wenmin Gong, Guangcun Lu. On coupled Dirac systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4329-4346. doi: 10.3934/dcds.2017185 |
[11] |
Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 25-34. doi: 10.3934/dcds.2011.31.25 |
[12] |
Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087 |
[13] |
Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic & Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1 |
[14] |
Andrea Cianchi, Adele Ferone. Improving sharp Sobolev type inequalities by optimal remainder gradient norms. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1363-1386. doi: 10.3934/cpaa.2012.11.1363 |
[15] |
Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623 |
[16] |
Samir Adly, Oanh Chau, Mohamed Rochdi. Solvability of a class of thermal dynamical contact problems with subdifferential conditions. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 91-104. doi: 10.3934/naco.2012.2.91 |
[17] |
M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072 |
[18] |
Feng Luo. A combinatorial curvature flow for compact 3-manifolds with boundary. Electronic Research Announcements, 2005, 11: 12-20. |
[19] |
Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223 |
[20] |
Carlos Fresneda-Portillo, Sergey E. Mikhailov. Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3059-3088. doi: 10.3934/cpaa.2019137 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]