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On one problem with free boundary for a nonlinear system

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Abstract

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”.

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Authors
  1. B. V. Bazalii
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  2. N. V. Krasnoshchek
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Additional information

Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1155–1165, September, 1996.

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Bazalii, B.V., Krasnoshchek, N.V. On one problem with free boundary for a nonlinear system. Ukr Math J 48, 1309–1321 (1996). https://doi.org/10.1007/BF02595354

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  • DOI: https://doi.org/10.1007/BF02595354

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