Abstract and Applied Analysis

Hyperbolic differential-operator equations on a whole axis

Yakov Yakubov

Abstract

We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time $t$ of the same order as equations. The case of stable solutions of abstract hyperbolic equations is treated. Then we show applications of obtained abstract results to hyperbolic differential equations which, in particular, may represent the longitudinal displacements of an inhomogeneous rod under the action of forces at the two ends which are proportional to the acceleration.

Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 2 (2004), 99-113.

Dates
First available in Project Euclid: 6 April 2004

https://projecteuclid.org/euclid.aaa/1081267502

Digital Object Identifier
doi:10.1155/S1085337504311103

Mathematical Reviews number (MathSciNet)
MR2058267

Zentralblatt MATH identifier
1096.34037

Subjects