The dam problem in unbounded domains

Summary The time dependent dam problem in a general unbounded domain is studied and an existence theorem is proved by means of a rather general approximation procedure. Moreover the propagation of the support of the solution is studied in a number of geometrical situations of interest. The corresponding stationary problem is also studied and an existence theorem is proved. Finally several one-dimensional examples are given in which the solution can be either written explicitely or found solving an ordinary differential equation.This work has been supported by MURST (Italy), by I.A.N.-C.N.R. of Pavia (Italy), and by SFB 123 of University of Heidelberg (Germany).