Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71454, Iran
Boundary Value Problems 2012, 2012:50 doi:10.1186/1687-2770-2012-50Published: 26 April 2012
We consider the semilinear Petrovsky equation
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.