a1 Imperial College, London
a2 Charles University, Prague
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.
(Received January 23 1980)
(Revised July 01 1980)
† The work of this author was carried out while visiting Brunel University and Oxford University Computing Laboratory, and was supported by The British Council.