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Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

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  • Nabil Merazga
  • Abdelfatah Bouziani

Abstract

This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable.

Suggested Citation

  • Nabil Merazga & Abdelfatah Bouziani, 2006. "Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-20, September.
    • Handle: RePEc:hin:jnijsa:034053
    DOI: 10.1155/JAMSA/2006/34053
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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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