论文信息 - A variational inequality approach to Hele-Shaw flow with a moving boundary

A variational inequality approach to Hele-Shaw flow with a moving boundary

This paper is concerned with the study of a mathematical model of the injection of fluid into a finite Hele–Shaw cell. The mathematical problem is one of solving Laplace's equation in an unknown region whose boundary changes with time. By a transformation of the dependent variable, an elliptic variational inequality formulation of the moving boundary problem is obtained. The variational inequality is shown to have a unique solution up to the time at which the cell is filled. Regularity results for the solution of the inequality are obtained by studying a penalty approximation of the inequality.

C. M. Elliott | C. Elliott | V. Janovský

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