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A mixed problem with only integral boundary conditions for a hyperbolic equation

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  • Abdelfatah Bouziani

Abstract

We investigate an initial boundary value problem for a second-order hyperbolic equation with only integral conditions. We show the existence, uniqueness, and continuous dependence of a strongly generalized solution. The proof is based on an energy inequality established in a nonclassical function space, and on the density of the range of the operator associated to the abstract formulation of the studied problem by introducing special smoothing operators.

Suggested Citation

  • Abdelfatah Bouziani, 2004. "A mixed problem with only integral boundary conditions for a hyperbolic equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:964830
    DOI: 10.1155/S0161171204204240
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