April  2001, 7(2): 385-396. doi: 10.3934/dcds.2001.7.385

3D wave equations in sphere-symmetric domain with periodically oscillating boundaries

1. 

Department of Mathematics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan

Revised  November 2000 Published  January 2001

IBVP for linear nonhomogeneous three dimensional wave equations is considered in sphere-symmetric domain with periodically moving boundaries. The unknown function and all data are assumed to be sphere-symmetric. The boundary data and the nonhomogeneous term are periodic. We shall define one dimensional dynamical system $A$, using the boundary functions. Then we shall show that under some Diophantine conditions on periods of the given data and the rotation number of $A$, every solution of IBVP is quasiperiodic in $t$.
Citation: Masaru Yamaguchi. 3D wave equations in sphere-symmetric domain with periodically oscillating boundaries. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 385-396. doi: 10.3934/dcds.2001.7.385
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