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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.
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.