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

Abdelfatah Bouziani

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-13

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:964830

DOI: 10.1155/S0161171204204240

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