arXiv 1307.01092013-07-02math.AP

带非线性源的发展椭圆Muskat-Verigin问题光滑界面的存在性

The existence of a smooth interface in the evolutionary elliptic Muskat--Verigin problem with nonlinear source

Sergey P. Degtyarev

备注：: This is an English translation of the article S.P. Degtyarev, The existence of a smooth interface in the Muskat-Verigin elliptic evolution problem with a nonlinear source, http://www.ams.org/mathscinet-getitem?mr=2809065

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摘要：

研究了具有非线性源的椭圆型方程的两相Muskat-Verigin自由边界问题.通过对自由边界上的一个条件进行抛物正则化，证明了光滑解和光滑自由边界的存在性。

英文摘要：

We study the two-phase Muskat--Verigin free-boundary problem for elliptic equations with nonlinear sources. The existence of a smooth solution and a smooth free boundary is proved locally in time by applying the parabolic regularization of a condition on the free boundary.

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