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On the solvability of parabolic and hyperbolic problems with a boundary integral condition

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  • Abdelfatah Bouziani

Abstract

We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear operator associated to the abstract formulation of the studied problem.

Suggested Citation

  • Abdelfatah Bouziani, 2002. "On the solvability of parabolic and hyperbolic problems with a boundary integral condition," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:627107
    DOI: 10.1155/S0161171202005860
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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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