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Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation

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  • Nabil Merazga
  • Abdelfatah Bouziani

Abstract

This paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by means of the Rothe method. Besides, convergence and an error estimate for a semidiscrete approximation are obtained.

Suggested Citation

  • Nabil Merazga & Abdelfatah Bouziani, 2003. "Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-24, January.
    • Handle: RePEc:hin:jnlaaa:639847
    DOI: 10.1155/S1085337503305019
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    Cited by:

    1. Gupta, Nishi & Maqbul, Md., 2019. "Solutions to Rayleigh–Love equation with constant coefficients and delay forcing term," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 123-134.

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