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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose


Mathematical Citation Quotient (MCQ) 2018: 0.62

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2353-0626
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Controllability of the Semilinear Heat Equation with Impulses and Delay on the State

Hugo Leiva
  • Leiva: Louisiana State University, College of Science, Math. Department, Baton Rouge, LA 70803-USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-16 | DOI: https://doi.org/10.1515/msds-2015-0004

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 → 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.

Keywords: interior approximate controllability; semilinear heat equation with impulses and delay; strongly continuous semigroup

References

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About the article

Received: 2015-05-20

Accepted: 2015-08-15

Published Online: 2015-10-16


Citation Information: Nonautonomous Dynamical Systems, Volume 2, Issue 1, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2015-0004.

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©2015 Hugo Leiva. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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