Open Access Research

Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term

Faramarz Tahamtani* and Mohammad Shahrouzi

Author Affiliations

Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71454, Iran

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Boundary Value Problems 2012, 2012:50 doi:10.1186/1687-2770-2012-50

Published: 26 April 2012

Abstract

We consider the semilinear Petrovsky equation

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in a bounded domain and prove the existence of weak solutions. Furthermore, we show that there are solutions under some conditions on initial data which blow up in finite time with non-positive initial energy as well as positive initial energy. Estimates of the lifespan of solutions are also given.

Mathematics Subject Classification (2000): 35L35; 35L75; 37B25.

Keywords:
viscoelasticity; existence; blow-up; life-span; negative initial energy; positive initial energy