Approximate controllability of semilinear reaction diffusion equations
Pages: 171 - 182, Issue 2, June 2012

doi:10.3934/mcrf.2012.2.171      Abstract        References        Full text (367.6K)           Related Articles

Hugo Leiva - Universidad de los Andes, Facultad de Ciencias, Departamento de Matemática, Mérida 5101, Venezuela (email)
Nelson Merentes - Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matemática, Caracas 1051, Venezuela (email)
José L. Sánchez - Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matem, Caracas 1051, Venezuela (email)

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.
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.
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.
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.
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.
15	K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim., 25 (1987), 715-722.
16	K. Naito, Approximate controllability for trajectories of semilinear control systems, J. of Optimization Theory and Appl., 60 (1989), 57-65.
17	M. H. Protter, Unique continuation for elliptic equations, Transaction of the American Mathematical Society, 95 (1960), 81-91.
18	D. L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), 636-739.
19	L. De Teresa, Approximate controllability of semilinear heat equation in $\mathbbR^N$, SIAM J. Control Optim., 36 (1998), 2128-2147.
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.
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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