651. A variational inequality approach to Hele-Shaw flow with a moving boundary
- Author
-
Vladimír Janovský and Charles M. Elliott
- Subjects
Mathematical optimization ,Variables ,Mathematical problem ,Laplace transform ,General Mathematics ,media_common.quotation_subject ,Boundary problem ,Boundary (topology) ,Hele-Shaw flow ,Transformation (function) ,Variational inequality ,Applied mathematics ,Mathematics ,media_common - Abstract
SynopsisThis 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.
- Published
- 1981