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On the controllability of parabolic systems with a nonlinear term involving the state and the gradient. (English) Zbl 1038.93041
This paper studies the controllability of a quasilinear parabolic equation in a bounded domain of n with Dirichlet boundary conditions. The controls are considered to be supported on a small open subset of the domain or on a small part of the boundary. The null and approximate controllability of the system at any time is proved if the nonlinear term f(y,y) grows slower than |y|log 3/2 (1+|y|+|y|)+|y|log 1/2 (1+|y|+|y|) at infinity. The proofs use global Carleman estimates, regularity results and fixed point theorems.
MSC:
93C20Control systems governed by PDE
93B05Controllability
35K55Nonlinear parabolic equations
35K05Heat equation