# IJPAM: Volume 52, No. 1 (2009)

ON THE ULTRA-HYPERBOLIC WAVE OPERATOR

Wanchak Satsanit, Amnuay Kananthai
Department of Mathematics
Faculty of Science
Chiang Mai University
Chiang Mai, 50200, THAILAND
e-mail: malamnka@science.cmu.ac.th

Abstract.In this paper, we study the generalized wave equation of the form

with the initial conditions

where , is the -dimensional Euclidean space, is the ultra-hyperbolic operator iterated times defined by

, is a positive constant, is a nonnegative integer, and are continuous and absolutely integrable functions. We obtain as a solution for such equation. Moreover, by -approximation we also obtain the asymptotic solution . In particularly, if we put and , the reduces to the solution of the beam equation