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Stefan problem for the laplace equation with regard for the curvature of the free boundary

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Abstract

We consider a nonstationary problem with free boundary for an elliptic equation in the case where the value of the required function on an unknown boundary is proportional to the curvature of this boundary. We prove the existence of a solution in the small with respect to time in the spaces of smooth functions.

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Authors
  1. B. V. Bazalii
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Additional information

Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1299–1315, October, 1997.

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Bazalii, B.V. Stefan problem for the laplace equation with regard for the curvature of the free boundary. Ukr Math J 49, 1465–1484 (1997). https://doi.org/10.1007/BF02487433

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  • DOI: https://doi.org/10.1007/BF02487433

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