Passage to the limit in a chain of the muskat problems(II)

Abstract

This paper is the continuation of the paper: “Passage to the limit in a chain of the Muskat problems(I)”. In spherically symmetric case one prove that for some class of initial data, generated by a chain of the Muskat problems, the solutions of smooth approximate problems converge to a weak solution of the Muskat problem. This weak solution can be regarded as interpretation of so-called finger phenomenon.

Keywords:

• Muskat problem
• finger phenomenon
• free boundary problem

^*Osaka University, Osaka, Japan

^†Moscow State University, Moscow, Russia

^*Osaka University, Osaka, Japan

^†Moscow State University, Moscow, Russia

Notes

^*Osaka University, Osaka, Japan

^†Moscow State University, Moscow, Russia