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Reaction-Diffusion in Nonsmooth and Closed Domains

Abstract

We investigate the Dirichlet problem for the parabolic equation in a nonsmooth and closed domain possibly formed with irregular surfaces and having a characteristic vertex point. Existence, boundary regularity, uniqueness, and comparison results are established. The main objective of the paper is to express the criteria for the well-posedness in terms of the local modulus of lower semicontinuity of the boundary manifold. The two key problems in that context are the boundary regularity of the weak solution and the question whether any weak solution is at the same time a viscosity solution.

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Correspondence to Ugur G Abdulla.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abdulla, U.G. Reaction-Diffusion in Nonsmooth and Closed Domains. Bound Value Probl 2007, 031261 (2006). https://doi.org/10.1155/2007/31261

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Weak Solution
  • Functional Equation