Open AccessExponential decay for solutions to semilinear damped wave equation
Author(s) -
Stéphane Gerbi,
Belkacem SaidHouari
Publication year - 2012
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2012.5.559
Subject(s) - bounded function , exponential decay , exponential growth , domain (mathematical analysis) , wave equation , damped wave , exponential function , mathematical analysis , function (biology) , mathematics , lyapunov function , exponential stability , physics , nonlinear system , quantum mechanics , evolutionary biology , biology
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov 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 [4]