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A general decay result in a quasilinear parabolic system with viscoelastic term. (English) Zbl 1244.45004

Summary: We consider a quasilinear parabolic system of the form

$A\left(t\right)|{u}_{t}{|}^{m-2}{u}_{t}-{\Delta }u+{\int }_{0}^{t}g\left(t-s\right){\Delta }u\left(x,s\right)ds=0,$

for $m\ge \phantom{\rule{3.33333pt}{0ex}}2,A\left(t\right)$ a bounded and positive definite matrix, and $g$ a continuously differentiable decaying function and establish a general decay result from which the usual exponential and polynomial decay results are only special cases.

##### MSC:
 45K05 Integro-partial differential equations
##### References:
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