Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition

Abstract and Applied Analysis

Hindawi Limited

Read this article at

ScienceOpenPublisher
Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition on a bounded domain with Lyapunov boundary is proved in the space of continuous functions up to boundary. Since a Green matrix of the problem is known, we may seek the solution as the linear combination of the single-layer potential, the volume potential, and the Poisson integral. Then the original problem may be reduced to a Volterra integral equation of the second kind associated with a compact operator. Classical analysis may be employed to show that the corresponding integral equation has a unique solution if the boundary data is continuous, the initial data is continuously differentiable, and the source term is Hölder continuous in the spatial variable. This in turn proves that the original problem has a unique solution.

      Related collections

      Most cited references 7

      • Record: found
      • Abstract: not found
      • Article: not found

      The random walk's guide to anomalous diffusion: a fractional dynamics approach

        Bookmark
        • Record: found
        • Abstract: not found
        • Article: not found

        Fractional diffusion and wave equations

         W. Schneider,  W. Wyss (1989)
          Bookmark
          • Record: found
          • Abstract: not found
          • Article: not found

          Cauchy problem for fractional diffusion equations

            Bookmark

            Author and article information

            Journal
            Abstract and Applied Analysis
            Abstract and Applied Analysis
            Hindawi Limited
            1085-3375
            1687-0409
            2011
            2011
            : 2011
            :
            : 1-11
            10.1155/2011/321903
            © 2011

            http://creativecommons.org/licenses/by/3.0/

            Comments

            Comment on this article