Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source
This paper is concerned with a nonlocal nonlinear diffusion equation with Dirichlet boundary condition and a source , , , , , , and , , which is analogous to the local porous medium equation. First, we prove the existence and uniqueness of the solution as well as the validity of a compariso...
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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/10.1155/2013/746086 |
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| _version_ | 1850224031456821248 |
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| author | Guosheng Zhang Yifu Wang |
| author_facet | Guosheng Zhang Yifu Wang |
| author_sort | Guosheng Zhang |
| collection | DOAJ |
| description | This paper is concerned with a nonlocal nonlinear diffusion equation with Dirichlet boundary condition and a source , , ,
, , , and , , which is analogous to the local porous medium equation. First, we prove the existence and uniqueness of the solution as well as the validity of a comparison principle. Next, we discuss the blowup phenomena of the solution to this problem. Finally, we discuss the blowup rates and sets of the solution. |
| format | Article |
| id | doaj-art-50cddeec41a244d6b5414f4cccdc4fdc |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-50cddeec41a244d6b5414f4cccdc4fdc2025-08-20T02:05:45ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/746086746086Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a SourceGuosheng Zhang0Yifu Wang1School of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Beijing Institute of Technology, Beijing 100081, ChinaThis paper is concerned with a nonlocal nonlinear diffusion equation with Dirichlet boundary condition and a source , , , , , , and , , which is analogous to the local porous medium equation. First, we prove the existence and uniqueness of the solution as well as the validity of a comparison principle. Next, we discuss the blowup phenomena of the solution to this problem. Finally, we discuss the blowup rates and sets of the solution.http://dx.doi.org/10.1155/2013/746086 |
| spellingShingle | Guosheng Zhang Yifu Wang Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source Abstract and Applied Analysis |
| title | Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source |
| title_full | Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source |
| title_fullStr | Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source |
| title_full_unstemmed | Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source |
| title_short | Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source |
| title_sort | blowup for nonlocal nonlinear diffusion equations with dirichlet condition and a source |
| url | http://dx.doi.org/10.1155/2013/746086 |
| work_keys_str_mv | AT guoshengzhang blowupfornonlocalnonlineardiffusionequationswithdirichletconditionandasource AT yifuwang blowupfornonlocalnonlineardiffusionequationswithdirichletconditionandasource |