Hiroshima Mathematical Journal

Investigation of the nonlocal initial boundary value problems for some hyperbolic equations

Abstract

In the present article we are interested in the analysis of nonlocal initial boundary value problems for some medium oscillation equations. More precisely, we investigate different types of nonlocal problems for one-dimensional oscillation equations and prove existence and uniqueness theorems. In some cases algorithms for direct construction of the solution are given. We also consider nonlocal problem for multidimensional hyperbolic equation and prove the uniqueness theorem for the formulated initial boundary value problem applying the theory of characteristics under rather general assumptions.

Article information

Source
Hiroshima Math. J., Volume 31, Number 3 (2001), 345-366.

Dates
First available in Project Euclid: 23 June 2006

https://projecteuclid.org/euclid.hmj/1151105723

Digital Object Identifier
doi:10.32917/hmj/1151105723

Mathematical Reviews number (MathSciNet)
MR1870980

Zentralblatt MATH identifier
1008.35037

Citation

Gordeziani, David; Avalishvili, Gia. Investigation of the nonlocal initial boundary value problems for some hyperbolic equations. Hiroshima Math. J. 31 (2001), no. 3, 345--366. doi:10.32917/hmj/1151105723. https://projecteuclid.org/euclid.hmj/1151105723