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Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities

Zuazua E.

Control and Cybernetics

1999

Vol. 28, no 3

665-683

We consider the semilinear heat equation involving gradient terms in a bounded domain of [R^n]. It is assumed that the non-linearity is globally Lipschitz. We prove that the system is approximately controllable when t1e control acts on a bounded subset of the domain. The proof uses a variant of a classical fixed point method and is a simpler alternative to the earlier proof existing in the literature by means of the penalization of an optimal control problem. We also prove that the contool may be built so that, in addition to the approximate controllability requirement, it ensures that the state reaches exactly a finite number of constraints.