On a hyperbolic equation of high order in a Banach space


The Cauchy problem for the hyperbolic equation with zero initial conditions is studied in a Banach space H. Here A and Ak are linear operators mapping H into H and A is the infinitesimal generator of a strongly continuous cosine family of bounded operators in H. This equation is a generalization of the equation describing the propagation of time-dependent acoustic waves in a wide class of media with dispersion and absorption. By means of the technique of strongly continuous cosine operator functions, existence and uniqueness of the solution of this problem arc established. © 1992, Khayyam Publishing. All rights reserved.

Publication Title

Differential and Integral Equations

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