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On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification

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  • Abdelfatah Bouziani

Abstract

This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established for the quasilinear problem, using an iterative process based on results obtained for the linear problem.

Suggested Citation

  • Abdelfatah Bouziani, 2003. "On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-17, January.
    • Handle: RePEc:hin:jnlaaa:307270
    DOI: 10.1155/S1085337503210010
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    Cited by:

    1. Dehghan, Mehdi, 2007. "The one-dimensional heat equation subject to a boundary integral specification," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 661-675.

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