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: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/109546 |
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| _version_ | 1832552406102048768 |
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| author | Pan Zheng Chunlai Mu Dengming Liu Xianzhong Yao Shouming Zhou |
| author_facet | Pan Zheng Chunlai Mu Dengming Liu Xianzhong Yao Shouming Zhou |
| author_sort | Pan Zheng |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-01112f1695854fca9f0a3a1930290ef1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-01112f1695854fca9f0a3a1930290ef12025-02-03T05:58:39ZengWileyAbstract 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/109546 |
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