Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions
We study a slow diffusive -Laplace equation in a bounded domain with the Neumann boundary conditions. A natural energy is associated to the equation. It is shown that the solution blows up in finite time with the nonpositive initial energy, based on an energy technique. Furthermore, under some assum...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/643819 |
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| _version_ | 1832554235985657856 |
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| author | Chengyuan Qu Bo Liang |
| author_facet | Chengyuan Qu Bo Liang |
| author_sort | Chengyuan Qu |
| collection | DOAJ |
| description | We study a slow diffusive -Laplace equation in a bounded domain with the Neumann boundary conditions. A natural energy is associated to the equation. It is shown that the solution blows up in finite time with the nonpositive initial energy, based on an energy technique. Furthermore, under some assumptions of initial data, we prove that the solutions with bounded initial energy also blow up. |
| format | Article |
| id | doaj-art-922fa5d9b27c4039bbf6d85e5c5947b1 |
| 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-922fa5d9b27c4039bbf6d85e5c5947b12025-02-03T05:52:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/643819643819Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary ConditionsChengyuan Qu0Bo Liang1Department of Mathematics, Dalian Nationalities University, Dalian 116600, ChinaSchool of Science, Dalian Jiaotong University, Dalian 116028, ChinaWe study a slow diffusive -Laplace equation in a bounded domain with the Neumann boundary conditions. A natural energy is associated to the equation. It is shown that the solution blows up in finite time with the nonpositive initial energy, based on an energy technique. Furthermore, under some assumptions of initial data, we prove that the solutions with bounded initial energy also blow up.http://dx.doi.org/10.1155/2013/643819 |
| spellingShingle | Chengyuan Qu Bo Liang Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions Abstract and Applied Analysis |
| title | Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions |
| title_full | Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions |
| title_fullStr | Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions |
| title_full_unstemmed | Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions |
| title_short | Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions |
| title_sort | blow up in a slow diffusive laplace equation with the neumann boundary conditions |
| url | http://dx.doi.org/10.1155/2013/643819 |
| work_keys_str_mv | AT chengyuanqu blowupinaslowdiffusivelaplaceequationwiththeneumannboundaryconditions AT boliang blowupinaslowdiffusivelaplaceequationwiththeneumannboundaryconditions |