Global existence and blow-up of solutions to the double nonlinear porous medium equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866916124119007232 |
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| author | Sabitbek, Bolys Torebek, Berikbol |
| author_facet | Sabitbek, Bolys Torebek, Berikbol |
| contents | In this study, we examine a double nonlinear porous medium equation subject to a novel nonlinearity condition within a bounded domain. First, we introduce the blow-up solution for the problem under consideration for the negative initial energy. By introducing a set of potential wells, we construct invariant sets of solutions for the double nonlinear porous medium equation. For subcritical and critical initial energy scenarios, we derive the global existence and asymptotic behavior of weak solutions, as well as blow-up phenomena occurring within a finite time for the positive solution to the double nonlinear porous medium equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_06896 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Global existence and blow-up of solutions to the double nonlinear porous medium equation Sabitbek, Bolys Torebek, Berikbol Analysis of PDEs 35K92, 35B44, 35A01 In this study, we examine a double nonlinear porous medium equation subject to a novel nonlinearity condition within a bounded domain. First, we introduce the blow-up solution for the problem under consideration for the negative initial energy. By introducing a set of potential wells, we construct invariant sets of solutions for the double nonlinear porous medium equation. For subcritical and critical initial energy scenarios, we derive the global existence and asymptotic behavior of weak solutions, as well as blow-up phenomena occurring within a finite time for the positive solution to the double nonlinear porous medium equation. |
| title | Global existence and blow-up of solutions to the double nonlinear porous medium equation |
| topic | Analysis of PDEs 35K92, 35B44, 35A01 |
| url | https://arxiv.org/abs/2104.06896 |