The Australian Journal of Mathematical Analysis and Applications

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Paper's Title:

Long Time Behavior for a Viscoelastic Problem with a Positive Definite Kernel


Nasser-eddine Tatar

King Fahd University of Petroleum and Mineral, Department of Mathematical Sciences,
Dhahran, 31261 Saudi Arabia


We study the asymptotic behavior of solutions for an integro-differential problem which arises in the theory of viscoelasticity. It is proved that solutions go to rest in an exponential manner under new assumptions on the relaxation function in the memory term. In particular, we consider a new family of kernels which are not necessarily decreasing.

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