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Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy

Authors :
Fenglong Sun
Yonghong Wu
Lishan Liu
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