Blow-up analysis in degenerate parabolic systems coupled via norm-type reactions

Abstract

This paper deals with a class of degenerate parabolic equations coupled via nonlinear reactions in -norm type, subject to null Dirichlet boundary conditions. Firstly, we give the existence and uniqueness of local classical solutions and the comparison principle. Secondly, we determine the critical exponents for the blow-up solutions. Thirdly, all of the uniform blow-up profiles are obtained for simultaneous blow-up solutions.

Keywords:

• degenerate parabolic systems
• critical blow-up exponents
• uniform blow-up profile

AMS Subject Classifications:

• 35K65
• 35K61
• 35B33
• 35B40

Acknowledgements

The authors would like to express their many thanks to the Editor and the Reviewers for their constructive and helpful suggestions.

Disclosure statement

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.