ABSTRACT
In this paper, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a nonlinear source term
where is a bounded domain in () with a Dirichlet boundary condition. Under suitable assumptions on the initial data and the relaxation function g, we obtain the global existence and finite time blow-up of solutions with initial data at low energy level (i.e. ), by using the Galerkin method, the concavity method and an improved potential well method involving time t. We also derive the upper bounds for the blow-up time. Finally, we obtain the existence of solutions which blow up in finite time with initial data at arbitrary energy level.
Acknowledgements
The authors would like to thank the referee for his/her very important comments that improved the results and the quality of the paper.
Notes
No potential conflict of interest was reported by the authors.