Blow-up time and boundary layer for solutions in parabolic equations with different diffusion

Abstract

This paper deals with parabolic equations with different diffusion coefficients and coupled nonlinear sources, subject to homogeneous Dirichlet boundary conditions. We give many results about blow-up solutions, including blow-up time estimates for all of the spatial dimensions, the critical non-simultaneous blow-up exponents, uniform blow-up profiles, blow-up sets, and boundary layer with or without standard conditions on nonlocal sources. The conditions are much weaker than the ones for the corresponding results in the previous papers.

Keywords:

• Blow-up time
• uniform blow-up profile
• boundary layer
• critical non-simultaneous blow-up exponent

AMS Subject Classifications:

• 35K57
• 35K60
• 35B40
• 35B33

Acknowledgements

The authors express their many thanks to the hospitality of Professor Bei Hu of University of Notre Dame.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is partially supported by NNSF of China [grant number 11201483], Shandong Provincial Natural Science Foundation, China, and the Fundamental Research Funds for the Central Universities [grant number 15CX08011A].