2026-06-02T06:06:50Zhttps://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 519.6 Controllability Parabolic equations Nonlinear gradient terms Análisis numérico 1206 Análisis Numérico 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. DGES Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:47:17Z 2023-06-20T16:47:17Z 2002 journal article https://hdl.handle.net/20.500.14352/56999 0363-0129 10.1137/S0363012901386465 eng PB96-0663 PB98-1134 BFM2000-1317 open access application/pdf SIAM PUBLICATIONS