3D wave equations in sphere-symmetric domain with periodically oscillating boundaries
Masaru Yamaguchi · Discrete and Continuous Dynamical Systems · 2001
IBVP for linear nonhomogeneous three dimensional wave equations isconsidered in sphere-symmetric domain with periodically movingboundaries. 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 givendata and the rotation number of $A$, every solution of IBVP is quasiperiodic in $t$.