On one problem with free boundary for a nonlinear system - Bazalii, B. V.; Krasnoshchok, M. V. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We formulate the filtration problem with free boundary as a problem with discontinuous nonlinearity for a degenerate elliptic or parabolic system. We prove that a solution of the Dirichlet problem exists in both cases. We study some qualitative properties of these solutions, e.g., the existence of “dead cores”.