Extinction and Nonextinction for the Fast Diffusion Equation
This paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of RN with N>2. For 0<m<1, under appropriate hypotheses, we show that m=p is the critical exponent of extinction for the weak solu...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/747613 |
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| _version_ | 1832563009539538944 |
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| author | Chunlai Mu Li Yan Yi-bin Xiao |
| author_facet | Chunlai Mu Li Yan Yi-bin Xiao |
| author_sort | Chunlai Mu |
| collection | DOAJ |
| description | This paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of RN with N>2. For 0<m<1, under appropriate hypotheses, we show that m=p is the critical exponent of extinction for the weak solution. Furthermore, we prove that the solution either extinct or nonextinct in finite time depends strongly on the initial data and the first eigenvalue of -Δ with homogeneous Dirichlet boundary. |
| format | Article |
| id | doaj-art-51737be8549540779661ffabe4f703d4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51737be8549540779661ffabe4f703d42025-02-03T01:21:11ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/747613747613Extinction and Nonextinction for the Fast Diffusion EquationChunlai Mu0Li Yan1Yi-bin Xiao2College of Mathematics and Physics, Chongqing University, Chongqing 400044, ChinaCollege of Mathematics and Physics, Chongqing University, Chongqing 400044, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, ChinaThis paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of RN with N>2. For 0<m<1, under appropriate hypotheses, we show that m=p is the critical exponent of extinction for the weak solution. Furthermore, we prove that the solution either extinct or nonextinct in finite time depends strongly on the initial data and the first eigenvalue of -Δ with homogeneous Dirichlet boundary.http://dx.doi.org/10.1155/2013/747613 |
| spellingShingle | Chunlai Mu Li Yan Yi-bin Xiao Extinction and Nonextinction for the Fast Diffusion Equation Abstract and Applied Analysis |
| title | Extinction and Nonextinction for the Fast Diffusion Equation |
| title_full | Extinction and Nonextinction for the Fast Diffusion Equation |
| title_fullStr | Extinction and Nonextinction for the Fast Diffusion Equation |
| title_full_unstemmed | Extinction and Nonextinction for the Fast Diffusion Equation |
| title_short | Extinction and Nonextinction for the Fast Diffusion Equation |
| title_sort | extinction and nonextinction for the fast diffusion equation |
| url | http://dx.doi.org/10.1155/2013/747613 |
| work_keys_str_mv | AT chunlaimu extinctionandnonextinctionforthefastdiffusionequation AT liyan extinctionandnonextinctionforthefastdiffusionequation AT yibinxiao extinctionandnonextinctionforthefastdiffusionequation |