Self-similar solutions for the Muskat equation

Self-similar solutions for the Muskat equation
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DOI：
10.1016/j.aim.2022.108294
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发表时间：
2021-09
期刊：
Advances in Mathematics
影响因子：
1.7
通讯作者：
Eduardo Garc'ia-Ju'arez;Javier G'omez-Serrano;H. Nguyen;B. Pausader
Eduardo Garc'ia-Ju'arez;Javier G'omez-Serrano;H. Nguyen;B. Pausader
中科院分区：
数学1区
文献类型：
--
作者：
Eduardo Garc'ia-Ju'arez;Javier G'omez-Serrano;H. Nguyen;B. Pausader

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我们证明了Muskat方程自相似解的存在性。这些溶液的参数为0<| s|≪1；它们是t= 0时斜率为s的精确角，在t= 0时在x处变得光滑。
We show the existence of self-similar solutions for the Muskat equation. These solutions are parameterized by 0<| s|≪ 1; they are exact corners of slope s at t= 0 and become smooth in x for t> 0.