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Approximate controllability for the semilinear heat equation involving gradient terms. (English) Zbl 0952.49003

From the summary: “The paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state \(y\) and its spatial gradient \(\nabla y\) and the control acts on a nonempty open subset of the domain. The proof relies on the fact that the nonlinearity is globally Lipschitz with respect to \((y,\nabla y)\). The approximate controllability is viewed as the limit of a sequence of optimal control problems. It is proved that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces”.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
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