On the asymptotic behavior of strongly damped wave equations

Yunlong Du, Xin Li, Chunyou Sun

Abstract


This paper is devoted to the asymptotic behavior of the semi-linear
strongly damped wave equation with forcing term only belongs to $H^{-1}$. Some refined decompositions of the solution have been
presented, which allow to remove the quasi-monotone condition
$f'(s)> -k$. The asymptotic regularity and existence of a finite-dimensional exponential attractor are established under the
usual assumptions.

Keywords


Asymptotic regularity; strongly damped wave equation; quasi-monotone condition; exponential attractor

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