Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq,  (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asy...

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Main Authors: Pan Zheng, Chunlai Mu, Dengming Liu, Xianzhong Yao, Shouming Zhou
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/109546
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spelling doaj-01112f1695854fca9f0a3a1930290ef12020-11-24T20:53:51ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/109546109546Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear SourcePan Zheng0Chunlai Mu1Dengming Liu2Xianzhong Yao3Shouming Zhou4School of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaSchool of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaWe investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq,  (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.http://dx.doi.org/10.1155/2012/109546
collection DOAJ
language English
format Article
sources DOAJ
author Pan Zheng
Chunlai Mu
Dengming Liu
Xianzhong Yao
Shouming Zhou
spellingShingle Pan Zheng
Chunlai Mu
Dengming Liu
Xianzhong Yao
Shouming Zhou
Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
Abstract and Applied Analysis
author_facet Pan Zheng
Chunlai Mu
Dengming Liu
Xianzhong Yao
Shouming Zhou
author_sort Pan Zheng
title Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
title_short Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
title_full Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
title_fullStr Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
title_full_unstemmed Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
title_sort blow-up analysis for a quasilinear degenerate parabolic equation with strongly nonlinear source
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq,  (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.
url http://dx.doi.org/10.1155/2012/109546
work_keys_str_mv AT panzheng blowupanalysisforaquasilineardegenerateparabolicequationwithstronglynonlinearsource
AT chunlaimu blowupanalysisforaquasilineardegenerateparabolicequationwithstronglynonlinearsource
AT dengmingliu blowupanalysisforaquasilineardegenerateparabolicequationwithstronglynonlinearsource
AT xianzhongyao blowupanalysisforaquasilineardegenerateparabolicequationwithstronglynonlinearsource
AT shoumingzhou blowupanalysisforaquasilineardegenerateparabolicequationwithstronglynonlinearsource
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