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1 Journal of Mathematics and Applications

1 2015

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Approximate controllability of the impulsive semilinear heat equation

Leiva H., Merentes N.

Journal of Mathematics and Applications

2015

Vol. 38

85--104

In this paper we apply Rothe's Fixed Point Theorem to prove the interior approximate controllability of the following semilinear impulsive Heat Equation [...] where k = 1, 2, . . . , p, Ω is a bounded domain in [...] is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u belongs to [...]. Under this condition we prove the following statement: For all open nonempty subsets ω of Ω the system is approximately controllable on [0, τ]. Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state z0 to an ϵ neighborhood of the nal state z1 at time τ > 0.