Abstract
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing 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].
Highlights
In this paper we are concerned by the following problem utt − ∆u − ω∆ut + μut = u|u|p−2 x ∈ Ω, t > 0
The present problem has been studied by Gazzola and Squassina [4]
The authors proved some results on the well-posedness and investigate the asymptotic behavior of solutions of problem (1.1)
Summary
The authors proved some results on the well-posedness and investigate the asymptotic behavior of solutions of problem (1.1). They showed the global existence and the polynomial decay property of solutions provided that the initial data are in the potential well, [4, Theorem 3.8]. He showed that solutions with negative initial energy blows up by ut |ut|m−2, in finite time.
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