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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(t)|u t | m-2 u t -Δu+ 0 t g(t-s)Δu(x,s)ds=0,

for m2,A(t) 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.

45K05Integro-partial differential equations
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