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.
Differential and Integral Equations
Varlamov, V., & Goldstein, J. (1992). On a hyperbolic equation of high order in a Banach space. Differential and Integral Equations, 5 (2), 255-260. Retrieved from https://digitalcommons.memphis.edu/facpubs/5251