Approximate controllability of semilinear impulsive strongly damped wave equation

Authors

Hanzel Larez
Hugo Leiva
Jorge Rebaza, Missouri State UniversityFollow
Addison Rios

Abstract

Rothe's fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space Z_1/2=D((−Δ)^1/2)×L²(Ω), where Ω is a bounded domain in Rⁿ (n ≥ 1). Under some conditions we prove the following statement: For all open nonempty subsets ω of Ω the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state z0 to a neighborhood of the final state z_{1M/sub> at time τ >0.}

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1515/jaa-2015-0005

Keywords

Semilinear impulsive strongly damped wave equation, approximate controllability, Rothe's fixed-point theorem

Publication Date

2015

Recommended Citation

Larez, Hanzel, Hugo Leiva, Jorge Rebaza, and Addison Ríos. "Approximate controllability of semilinear impulsive strongly damped wave equation." Journal of Applied Analysis 21, no. 1 (2015): 45-57.

Journal Title

Journal of Applied Analysis