A new blow-up condition for semi-linear edge degenerate parabolic equation with singular potentials

Abstract

In this paper, we consider a class of semi-linear edge degenerate parabolic equation with singular potentials, which was proposed by Chen and Liu [Asymptotic stability and blow-up of solutions for semi-linear edge-degenerate parabolic equation with singular potentials. Discrete Contin. Dyn. Syst. 2016; 26:661–682.] in which the authors proved the solutions of the model blow up in finite time with low initial energy and critical initial energy. By constructing a new functional, we obtain a new blow-up condition, which demonstrates the possibility of finite time blow-up when the initial energy is larger than the critical initial energy.

Keywords:

• Semi-linear edge degenerate parabolic equation
• Singular potentials
• Blow-up
• Nehari manifold

AMS Subject Classifications:

• 35B33
• 35K50
• 35K55
• 35K63

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the Fundamental Research Funds for the Central Universities [grant number XDJK2015A16]; NSFC [grant number 11201380]; Project funded by China Postdoctoral Science Foundation [grant number 2014M550453], [grant number 2015T80948] and the Second Foundation for Young Teachers in Universities of Chongqing.