Mixed problem with integral conditions for a certain class of hyperbolic equations. (English) Zbl 0988.35103

Mesloub, Said; Bouziani, Abdelfatah

J. Appl. Math. 1, No. 3, 107-116 (2001).

Summary: We study a mixed problem with purely integral conditions for a class of two-dimensional second-order hyperbolic equations. We prove the existence, uniqueness, and the continuous dependence upon the data of a generalized solution. We use a functional analysis method based on a priori estimate and on the density of the range of the operator generated by the considered problem.

MSC:

35L20	Initial-boundary value problems for second-order hyperbolic equations
35D05	Existence of generalized solutions of PDE (MSC2000)

Keywords:

integral conditions; two-dimensional second-order hyperbolic equations; continuous dependence upon the data; functional analysis method