Uniform Blow-up Behavior for Degenerate and Singular Parabolic Equations

doi:10.13371/j.cnki.chin.q.j.m.2016.02.003

Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (2): 125-138.doi: 10.13371/j.cnki.chin.q.j.m.2016.02.003

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Uniform Blow-up Behavior for Degenerate and Singular Parabolic Equations

College of Science,China University of Petroleum

Received:2014-03-27 Online:2016-06-30 Published:2020-11-06
About author:LIU Bing-chen(1976-), male, native of Weifang, Shandong, an associate professor of China University of Petroleum, Ph.D., engages in partial differential equations.
Supported by:
Supported by the National Natural Science Foundation of China(11201483)； Supported by the Natural Science Foundation of Shandong Province； Supported by the Fundamental Research Funds for the Central Universities；

Abstract

Abstract: This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blowup exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases.

Key words: egenerate and singular parabolic equations, critical blow-up exponents, uniform blow-up behavior

CLC Number:

O175.26

LIU Bing-chen, ZHANG Chang-cheng. Uniform Blow-up Behavior for Degenerate and Singular Parabolic Equations[J]. Chinese Quarterly Journal of Mathematics, 2016, 31(2): 125-138.

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Uniform Blow-up Behavior for Degenerate and Singular Parabolic Equations

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