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Controllability of the Semilinear Heat Equation with Impulses and Delay on the State

Abstract:

In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay where ω is a bounded domain in RN(N ≥ 1), φ: [-r, 0] × ω → ? is a continuous function, ! is an open nonempty subset of ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(ω;)). Here r ≥ 0 is the delay and the nonlinear functions f, Ik: [0, τ] × ? × ? → ? are smooth enough, such that Under this condition we prove the following statement: For all open nonempty subset ! of ω the system is approximately controllable on [0, τ], for all τ > 0.