Exponential decay for solutions to semilinear damped wave equation

Stéphane Gerbi (1) , Belkacem Said-Houari (2)

1 LAMA - Laboratoire de Mathématiques
2 UBMA - Université Badji Mokhtar [Annaba]

This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyaponuv function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in an article of Gazzola and Squassina.

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete and Continuous Dynamical Systems - Series S, 2012, 5 (3), pp.559 - 566. ⟨10.1016/j.cam.2009.08.068⟩. ⟨hal-00348327v3⟩