2016-05-132016-05-132002Doubova Krasotchenko, A., Fernández Cara, E., González Burgos, M. y Zuazua Iriondo, E. (2002). On the controllability of parabolic systems with a nonlinear term involving the state and the gradient.0363-01291095-7138http://hdl.handle.net/11441/41189We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN 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, ∇y) grows slower than |y| log3/2(1+ |y|+ |∇y|)+ |∇y| log1/2(1+ |y|+ |∇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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/ControllabilityParabolic equationsNonlinear gradient termsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1137/S0363012901386465https://idus.us.es/xmlui/handle/11441/41189