2026-06-29T07:49:47Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/569992023-08-28T05:07:57Zcom_20.500.14352_14col_20.500.14352_15

On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient Doubova, Anna Fernández Cara, E. González Burgos, Manuel Zuazua Iriondo, Enrique 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. 2023-06-20T16:47:17Z 2023-06-20T16:47:17Z 2002 journal article 0363-0129 10.1137/S0363012901386465 https://hdl.handle.net/20.500.14352/56999 http://epubs.siam.org/sicon/resource/1/sjcodc/v41/i3/p798_s1 eng PB96-0663 PB98-1134 BFM2000-1317 open access SIAM PUBLICATIONS