Blow-up of solutions to a parabolic system with nonlocal source

Abstract

This paper deals with a parabolic system with different diffusion coefficients and coupled nonlocal sources, subject to homogeneous Dirichlet boundary conditions. The conditions on global existence, simultaneous or non-simultaneous blow-up, blow-up set, uniform blow-up profiles and boundary layer are got using comparison principle and asymptotic analysis methods.

Keywords:

• Parabolic system with variable coefficient and nonlocal source
• global existence
• blow-up
• blow-up profiles
• boundary layer

AMS Subject Classifications:

• 35K57
• 35K60
• 35B40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by Basic and Advanced Research Project of CQC-STC [grant number cstc2016jcyjA0018]; Fundamental Research Funds for the Central Universities [grant number XDJK2016E120], [grant number XDJK2015A16]; Project funded by China Postdoctoral Science Foundation [grant number 2014M550453], [grant number 2015T80948]; NSFC [grant number 11201380].