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

Abstract

We consider the semilinear Petrovsky equationin 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.

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