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  • Research Article
  • Open Access

Reaction-Diffusion in Nonsmooth and Closed Domains

Boundary Value Problems20062007:031261

  • Received: 31 May 2006
  • Accepted: 21 September 2006
  • Published:


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.


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


Authors’ Affiliations

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA


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© Ugur G. Abdulla 2007

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