Uniform Blow-up Behavior for Degenerate and Singular Parabolic Equations

LIU Bing-chen, ZHANG Chang-cheng

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

Uniform Blow-up Behavior for Degenerate and Singular Parabolic Equations

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College of Science,China University of Petroleum

LIU Bing-chen(1976-), male, native of Weifang, Shandong, an associate professor of China University of Petroleum, Ph.D., engages in partial differential equations.

Received date: 2014-03-27

Online published: 2020-11-06

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；

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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

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

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