TY - JOUR
T1 - Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms
AU - Cabanillas, V. R.
AU - De Menezes, S. B.
AU - Zuazua, E.
N1 - Funding Information:
1The work of the first author was partially supported by CNPq, Brazil. The work of the second author was supported by the European Union via the Alpha Project on Modeling and Engineering Mathematics. The work of the third author was supported by Grant PB 96-0663 of the DGES, Spain. 2The authors thank Professor L. A. Medeiros for encouragement and fruitful discussions. 3Lecturer, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil. 4Assistant Professor, Departamento de Matemática, Universidade Federal do Pará, Belém, Brazil. 5Professor, Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain. 6Dedicated to the memory of J.-L. Lions.
PY - 2001/8
Y1 - 2001/8
N2 - We consider the null controllability problem for the semi-linear heat equation with nonlinearities involving gradient terms in an unbounded domain Ω of ℝN with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain ω such that the uncontrolled region Ω\ω is bounded. Using Carleman inequalities, we prove first the null controllability of the linearized equation. Then, by a fixed-point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is C1 and globally Lipschitz, the system is null controllable.
AB - We consider the null controllability problem for the semi-linear heat equation with nonlinearities involving gradient terms in an unbounded domain Ω of ℝN with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain ω such that the uncontrolled region Ω\ω is bounded. Using Carleman inequalities, we prove first the null controllability of the linearized equation. Then, by a fixed-point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is C1 and globally Lipschitz, the system is null controllable.
KW - Approximate controllability
KW - Carleman inequalities
KW - Null controllability
KW - Observability inequality
KW - Unbounded domains
UR - https://www.scopus.com/pages/publications/0035536763
U2 - 10.1023/A:1017515027783
DO - 10.1023/A:1017515027783
M3 - Artículo (Contribución a Revista)
AN - SCOPUS:0035536763
SN - 0022-3239
VL - 110
SP - 245
EP - 264
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -