A mixed problem with only integral boundary conditions for ahyperbolic equation

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.

Identifiers

DOI

10.1155/s0161171204204240

Citations and references