Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations
This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations ut−βuxx−kuxxt+γuxxxx=fuxx. At low initial energy level (Ju0<d), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approxim...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6668355 |
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| author | Huafei Di Zefang Song |
| author_facet | Huafei Di Zefang Song |
| author_sort | Huafei Di |
| collection | DOAJ |
| description | This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations ut−βuxx−kuxxt+γuxxxx=fuxx. At low initial energy level (Ju0<d), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approximation and potential well methods but also obtain the finite time blow-up result by adopting the potential well and improved concavity skills. Finally, we also discussed the finite time blow-up phenomenon for certain solutions of these problems with high initial energy. |
| format | Article |
| id | doaj-art-8ef0783bcbc7467481283aa28f24c817 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8ef0783bcbc7467481283aa28f24c8172025-02-03T01:00:15ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66683556668355Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic EquationsHuafei Di0Zefang Song1School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, ChinaSchool of Economics and Statistics, Guangzhou University, Guangzhou 510006, ChinaThis paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations ut−βuxx−kuxxt+γuxxxx=fuxx. At low initial energy level (Ju0<d), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approximation and potential well methods but also obtain the finite time blow-up result by adopting the potential well and improved concavity skills. Finally, we also discussed the finite time blow-up phenomenon for certain solutions of these problems with high initial energy.http://dx.doi.org/10.1155/2021/6668355 |
| spellingShingle | Huafei Di Zefang Song Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations Advances in Mathematical Physics |
| title | Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations |
| title_full | Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations |
| title_fullStr | Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations |
| title_full_unstemmed | Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations |
| title_short | Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations |
| title_sort | initial and boundary value problems for a class of nonlinear metaparabolic equations |
| url | http://dx.doi.org/10.1155/2021/6668355 |
| work_keys_str_mv | AT huafeidi initialandboundaryvalueproblemsforaclassofnonlinearmetaparabolicequations AT zefangsong initialandboundaryvalueproblemsforaclassofnonlinearmetaparabolicequations |