Back to Search
Start Over
Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy
- Source :
- SN Partial Differential Equations and Applications. 1
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, a linear weak damping and superlinear source. Finite time blow-up results have been obtained for the case in which the initial energy $$E(0)\le M$$ , where M is a positive constant. By utilizing Levine’s classical concavity method, we give a new blow-up criterion which includes the case of $$E(0)>M$$ and derive an explicit upper bound for the blow-up time. By using the Fountain Theorem, we show that the problem with arbitrary positive initial energy always admits weak solutions blowing up in finite time.
Details
- ISSN :
- 26622971 and 26622963
- Volume :
- 1
- Database :
- OpenAIRE
- Journal :
- SN Partial Differential Equations and Applications
- Accession number :
- edsair.doi...........54dfa405c02dadc4bc42437961cce9de
- Full Text :
- https://doi.org/10.1007/s42985-020-00031-1