Approximate controllability of semilinear impulsive strongly damped wave equation

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<inf>1/2</inf> = 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 z<inf>0</inf> to a neighborhood of the final state z<inf>1</inf> at time τ > 0.

Año de publicación:

2015

Keywords:

• Approximate controllability
• Semilinear impulsive strongly damped wave equation
• Rothe's fixed point theorem

Fuente:

scopus

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