Abstract and Applied Analysis
Volume 2004 (2004), Issue 2, Pages 99-113
Hyperbolic differential-operator equations on a whole axis
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel
Received 24 August 2003
Copyright © 2004 Yakov Yakubov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 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.