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A One-Dimensional Parabolic Problem Arising in Studies of Some Free Boundary Problems

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Abstract

The paper is concerned with a one-dimensional parabolic problem in a domain bounded by two lines x = 0 and x = kt, k > 0, (x, t) ∈ ℝ2, with the Neumann boundary condition on the line x = 0 and with dynamic boundary condition on the line x = kt. For the solution of this problem, a coercive estimate in a weighted Hölder norm is obtained. It is shown that this estimate can be useful for the analysis of parabolic free boundary problems. Bibliography: 7 titles.

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Authors and Affiliations

  1. St.Petersburg Department of the, Steklov Mathematical Institute, Russia

    V. A. Solonnikov

  2. Department of Mathmatics, University of Florence, Italy

    A. Fasano

Authors
  1. V. A. Solonnikov
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  2. A. Fasano
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Solonnikov, V.A., Fasano, A. A One-Dimensional Parabolic Problem Arising in Studies of Some Free Boundary Problems. Journal of Mathematical Sciences 115, 2066–2075 (2003). https://doi.org/10.1023/A:1022616300191

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  • DOI: https://doi.org/10.1023/A:1022616300191

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