Doubly Degenerate Equation Arising in Fresh-Salt Water Flow with Pumping

摘要

In the paper the authors study the Cauchy problem that arises in a twodimensional groundwater flow problem. The physical background is given in Section 2. In section 3 it is shown that the solution satisfies a contraction property. It then follows immediately that the problem has at most one solution. The existence result is established via approximation in Section 4. A method based on a level line argument is used to get a gradient bound which is crucial for the existence. The method is first used in Blanc for a related problem (the injection case).