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

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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 → ℝ 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] × ℝ × ℝ → ℝ 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.
Opis fizyczny
  • Leiva: Louisiana State University, College of Science, Math. Department, Baton Rouge, LA 70803-USA
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