A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up
| Title: | A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up |
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| Authors: | Deng, Qigang, Zeng, Fugeng, Jiang, Min |
| Source: | Comptes Rendus. Mécanique, Vol 350, Iss G2, Pp 269-282 (2022) |
| Publisher Information: | Académie des sciences, 2022. |
| Publication Year: | 2022 |
| Collection: | LCC:Materials of engineering and construction. Mechanics of materials |
| Subject Terms: | Logarithmic nonlinearity, Non-Newton filtration equation, Singular potential, Global existence, Blow-up, Materials of engineering and construction. Mechanics of materials, TA401-492 |
| More Details: | In this paper, we study the initial-boundary value problem of the singular non-Newton filtration equation with logarithmic nonlinearity. By using the concavity method, we obtain the existence of finite time blow-up solutions at initial energy $J(u_0) \leqslant d$. Furthermore, we discuss the asymptotic behavior of the weak solution and prove that the weak solution converges to the corresponding stationary solution as $t\rightarrow +\infty $. Finally, we give sufficient conditions for global existence and blow-up of solutions at initial energy $J(u_0)>d$. |
| Document Type: | article |
| File Description: | electronic resource |
| Language: | English French |
| ISSN: | 1873-7234 |
| Relation: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.117/; https://doaj.org/toc/1873-7234 |
| DOI: | 10.5802/crmeca.117 |
| Access URL: | https://doaj.org/article/17d9db7744524cf6a232ac3cf2d172b0 |
| Accession Number: | edsdoj.17d9db7744524cf6a232ac3cf2d172b0 |
| Database: | Directory of Open Access Journals |
| ISSN: | 18737234 |
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| DOI: | 10.5802/crmeca.117 |
| Published in: | Comptes Rendus. Mécanique |
| Language: | English French |