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Contrôlabilité approchée de l’équation de la chaleur semi- linéaire. (Approximate controllability for the semilinear heat equation). (French. Abridged English version) Zbl 0770.35009
Summary: This note is concerned with the study of the approximate controllability problem for the semilinear heat equation in a bounded domain $$\Omega$$ with homogeneous Dirichlet boundary conditions when the control acts on any open and nonempty subset of $$\Omega$$. The approximate controllability in $$L^ p(\Omega)$$ for $$1<p<+\infty$$ is proved when the nonlinearity is globally Lipschitz.

##### MSC:
 35B37 PDE in connection with control problems (MSC2000) 35K05 Heat equation 49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 35K55 Nonlinear parabolic equations