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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6668355 |
| Summary: | 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. |
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| ISSN: | 1687-9139 |