Approximate controllability of semilinear impulsive strongly damped wave equation
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 Z1/2=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 z1M/sub> at time τ >0.
Semilinear impulsive strongly damped wave equation, approximate controllability, Rothe's fixed-point theorem
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 of Applied Analysis