Abstract
One considers the damped semilinear viscoelastic wave equation $$u_{tt}-\Delta u+\alpha u+f(u)+\int_0^tg(t-\tau )\Delta u(\tau )\, d\tau +h(u_t)=0\,\,\,\hbox{in}\,\,\,\Omega\times (0,\infty ),$$ where $\Omega$ is any bounded or finite measure domain of ${\bf R}^ n$, $\alpha\geq 0$ and $f,h$ are power like functions. The existence of global regular and weak solutions is proved by means of the Faedo-Galerkin method and uniform decay rates of the energy are obtained following the perturbed energy method by assuming that $g$ decays exponentially.
Citation
M. M. Cavalcanti. V. N. Domingos Cavalcanti. T. F. Ma. J. A. Soriano. "Global existence and asymptotic stability for viscoelastic problems." Differential Integral Equations 15 (6) 731 - 748, 2002. https://doi.org/10.57262/die/1356060814
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