| Autor: |
Jingjie Wang, Xiaoyong Wen, Manwai Yuen |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 7, Iss 8, Pp 15313-15330 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2022839?viewType=HTML |
| Popis: |
In this paper, under the assumption of an initial bounded region $ \Omega(0) $, we establish the blowup phenomenon of the regular solutions and $ C^{1} $ solutions to the two-phase model in $ \mathbb{R}^{N} $. If the total energy $ E $ and the total mass $ M > 0 $ satisfy $ \begin{equation} \nonumber \max\limits_{\vec{x_{0}}\in\partial\Omega(0)}\sum\limits_{i = 1}^{N}u_{i}^{2}(0,\vec{x_{0}}) 0 $, then the blowup of the solutions to the two-phase model will be formed in finite time in $ \mathbb{R}^{N} $. Furthermore, under the assumptions that the radially symmetric initial data and initial density contain vacuum states, the blowup of the smooth solutions to the two-phase model will be formed in finite time in $ \mathbb{R}^{N} (N \geq2) $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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