On one problem with free boundary for a nonlinear system
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”.
English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 9, pp 1309-1321.
Citation Example: Bazalii B. V., Krasnoshchok M. V. On one problem with free boundary for a nonlinear system // Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1155–1165.