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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.

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