Nonlinear spectral theory and controllability of semilinear evolution equations

Abstract:

In this paper we introduce and apply a new nonlinear spectrum to characterize theexact controllability for a semilinear evolution equation. To this end, we firs recalla necessary and sufficien condition for the exact controllability of the correspondinglinear system and prove that, under suitable hypotheses on the nonlinear right-handside, the exact controllability of the linear system carries over to the perturbated semilinearsystem. Afterwards we apply this result to a nonlinear damped wave equation. © 2012 Nova Science Publishers, Inc. All rights reserved.

Año de publicación:

2011

Keywords:

• Nonlinear spectral theory
• exact controllability
• Semilinear volution equation

Fuente:

scopus