RT Journal Article
T1 On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient
A1 Doubova, Anna
A1 Fernández Cara, E.
A1 González Burgos, Manuel
A1 Zuazua Iriondo, Enrique
AB We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of ${\mathbb R}^N$ with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term $f( y, \nabla y)$ grows slower than $|y| \log^{3/2}(1+ |y| + |\nabla y|) + |\nabla y| \log^{1/2}(1+ |y| + |\nabla y|)$ at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.
PB SIAM PUBLICATIONS
SN 0363-0129
YR 2002
FD 2002
LK https://hdl.handle.net/20.500.14352/56999
UL https://hdl.handle.net/20.500.14352/56999
LA eng
NO DGES
DS Docta Complutense
RD 23 dic 2025