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The simplest semilinear parabolic equation of normal type
Approximate controllability of semilinear reaction diffusion equations
1. | Universidad de los Andes, Facultad de Ciencias, Departamento de Matemática, Mérida 5101, Venezuela |
2. | Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matemática, Caracas 1051, Venezuela |
3. | Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matem, Caracas 1051, Venezuela |
References:
[1] |
J. Appell, H. Leiva, N. Merentes and A. Vignoli, Un espectro de compresión no lineal con aplicaciones a la controlabilidad aproximada de sistemas semilineales,, preprint., ().
|
[2] |
S. Axler, P. Bourdon and W. Ramey, "Harmonic Function Theory," Graduate Texts in Math., 137, Springer Verlag, New York, 1992. |
[3] |
D. Barcenas, H. Leiva and Z. Sívoli, A broad class of evolution equations are approximately controllable, but never exactly controllable, IMA J. Math. Control Inform., 22 (2005), 310-320.
doi: 10.1093/imamci/dni029. |
[4] |
D. Barcenas, H. Leiva and W. Urbina, Controllability of the Ornstein-Uhlenbeck equation, IMA J. Math. Control Inform., 23 (2006), 1-9. |
[5] |
D. Barcenas, H. Leiva, Y. Quintana and W. Urbina, Controllability of Laguerre and Jacobi equations, International Journal of Control, 80 (2007), 1307-1315.
doi: 10.1080/00207170701294581. |
[6] |
R. F. Curtain and A. J. Pritchard, "Infinite Dimensional Linear Systems," Lecture Notes in Control and Information Sciences, 8, Springer Verlag, Berlin, 1978. |
[7] |
R. F. Curtain and H. J. Zwart, "An Introduction to Infinite Dimensional Linear Systems Theory," Text in Applied Mathematics, 21, Springer Verlag, New York, 1995. |
[8] |
C. Fabre, J. P. Puel and E. Zuazua, Approximate controllability of semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), 31-61.
doi: 10.1017/S0308210500030742. |
[9] |
J. I. Díaz, J. Henry and A. M. Ramos, On the approximate controllability of some semilinear parabolic boundary-value problems, Appl. Math. Optim., 37 (1998), 71-97.
doi: 10.1007/s002459900069. |
[10] |
E. Fernandez-Cara, Remark on approximate and null controllability of semilinear parabolic equations, ESAIM: Proceeding of Controle et Equations aux Derivees Partielles, 4 (1998), 73-81. |
[11] |
E. Fernandez-Cara and E. Zuazua, Controllability for blowing up semilinear parabolic equations, C. R. Acad. Sci. Paris Sér I Math., 330 (2000), 199-204. |
[12] |
L. Hormander, "Linear Partial Differential Equations," Springer Verlag, 1969. |
[13] |
H. Leiva, N. Merentes and J. L. Sanchez, Interior controllability of the $nD$ semilinear heat equation, African Diaspora Journal of Mathematics, Special Vol. in Honor of Profs. C. Corduneanu, A. Fink and S. Zaidman., 12 (2011), 1-12. |
[14] |
H. Leiva and Y. Quintana, Interior controllability of a broad class of reaction diffusion equations, Mathematical Problems in Engineering, 2009, Article ID 708516, 8 pp.
doi: 10.1155/2009/708516. |
[15] |
K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim., 25 (1987), 715-722.
doi: 10.1137/0325040. |
[16] |
K. Naito, Approximate controllability for trajectories of semilinear control systems, J. of Optimization Theory and Appl., 60 (1989), 57-65.
doi: 10.1007/BF00938799. |
[17] |
M. H. Protter, Unique continuation for elliptic equations, Transaction of the American Mathematical Society, 95 (1960), 81-91.
doi: 10.1090/S0002-9947-1960-0113030-3. |
[18] |
D. L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), 636-739.
doi: 10.1137/1020095. |
[19] |
L. De Teresa, Approximate controllability of semilinear heat equation in $\mathbbR^N$, SIAM J. Control Optim., 36 (1998), 2128-2147.
doi: 10.1137/S036012997322042. |
[20] |
L. De Teresa and E. Zuazua, Approximate controllability of semilinear heat equation in unbounded domains, Nonlinear Anal., 8 (1999). |
[21] |
Xu Zhang, A remark on null exact controllability of the heat equation, SIAM J. Control Optim., 40 (2001), 39-53.
doi: 10.1137/S0363012900371691. |
[22] |
E. Zuazua, Controllability of a system of linear thermoelasticity, J. Math. Pures Appl., 74 (1995), 291-315. |
[23] |
E. Zuazua, Control of partial differential equations and its semi-discrete approximation, Discrete and Continuous Dynamical Systems, 8 (2002), 469-513. |
show all references
References:
[1] |
J. Appell, H. Leiva, N. Merentes and A. Vignoli, Un espectro de compresión no lineal con aplicaciones a la controlabilidad aproximada de sistemas semilineales,, preprint., ().
|
[2] |
S. Axler, P. Bourdon and W. Ramey, "Harmonic Function Theory," Graduate Texts in Math., 137, Springer Verlag, New York, 1992. |
[3] |
D. Barcenas, H. Leiva and Z. Sívoli, A broad class of evolution equations are approximately controllable, but never exactly controllable, IMA J. Math. Control Inform., 22 (2005), 310-320.
doi: 10.1093/imamci/dni029. |
[4] |
D. Barcenas, H. Leiva and W. Urbina, Controllability of the Ornstein-Uhlenbeck equation, IMA J. Math. Control Inform., 23 (2006), 1-9. |
[5] |
D. Barcenas, H. Leiva, Y. Quintana and W. Urbina, Controllability of Laguerre and Jacobi equations, International Journal of Control, 80 (2007), 1307-1315.
doi: 10.1080/00207170701294581. |
[6] |
R. F. Curtain and A. J. Pritchard, "Infinite Dimensional Linear Systems," Lecture Notes in Control and Information Sciences, 8, Springer Verlag, Berlin, 1978. |
[7] |
R. F. Curtain and H. J. Zwart, "An Introduction to Infinite Dimensional Linear Systems Theory," Text in Applied Mathematics, 21, Springer Verlag, New York, 1995. |
[8] |
C. Fabre, J. P. Puel and E. Zuazua, Approximate controllability of semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), 31-61.
doi: 10.1017/S0308210500030742. |
[9] |
J. I. Díaz, J. Henry and A. M. Ramos, On the approximate controllability of some semilinear parabolic boundary-value problems, Appl. Math. Optim., 37 (1998), 71-97.
doi: 10.1007/s002459900069. |
[10] |
E. Fernandez-Cara, Remark on approximate and null controllability of semilinear parabolic equations, ESAIM: Proceeding of Controle et Equations aux Derivees Partielles, 4 (1998), 73-81. |
[11] |
E. Fernandez-Cara and E. Zuazua, Controllability for blowing up semilinear parabolic equations, C. R. Acad. Sci. Paris Sér I Math., 330 (2000), 199-204. |
[12] |
L. Hormander, "Linear Partial Differential Equations," Springer Verlag, 1969. |
[13] |
H. Leiva, N. Merentes and J. L. Sanchez, Interior controllability of the $nD$ semilinear heat equation, African Diaspora Journal of Mathematics, Special Vol. in Honor of Profs. C. Corduneanu, A. Fink and S. Zaidman., 12 (2011), 1-12. |
[14] |
H. Leiva and Y. Quintana, Interior controllability of a broad class of reaction diffusion equations, Mathematical Problems in Engineering, 2009, Article ID 708516, 8 pp.
doi: 10.1155/2009/708516. |
[15] |
K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim., 25 (1987), 715-722.
doi: 10.1137/0325040. |
[16] |
K. Naito, Approximate controllability for trajectories of semilinear control systems, J. of Optimization Theory and Appl., 60 (1989), 57-65.
doi: 10.1007/BF00938799. |
[17] |
M. H. Protter, Unique continuation for elliptic equations, Transaction of the American Mathematical Society, 95 (1960), 81-91.
doi: 10.1090/S0002-9947-1960-0113030-3. |
[18] |
D. L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), 636-739.
doi: 10.1137/1020095. |
[19] |
L. De Teresa, Approximate controllability of semilinear heat equation in $\mathbbR^N$, SIAM J. Control Optim., 36 (1998), 2128-2147.
doi: 10.1137/S036012997322042. |
[20] |
L. De Teresa and E. Zuazua, Approximate controllability of semilinear heat equation in unbounded domains, Nonlinear Anal., 8 (1999). |
[21] |
Xu Zhang, A remark on null exact controllability of the heat equation, SIAM J. Control Optim., 40 (2001), 39-53.
doi: 10.1137/S0363012900371691. |
[22] |
E. Zuazua, Controllability of a system of linear thermoelasticity, J. Math. Pures Appl., 74 (1995), 291-315. |
[23] |
E. Zuazua, Control of partial differential equations and its semi-discrete approximation, Discrete and Continuous Dynamical Systems, 8 (2002), 469-513. |
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