Doubova, AnnaFernández Cara, E.González Burgos, ManuelZuazua Iriondo, Enrique2023-06-202023-06-2020020363-012910.1137/S0363012901386465https://hdl.handle.net/20.500.14352/56999We 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.engjournal articlehttp://epubs.siam.org/sicon/resource/1/sjcodc/v41/i3/p798_s1open access519.6ControllabilityParabolic equationsNonlinear gradient termsAnálisis numérico1206 Análisis Numérico