One dimensional wave equations in domain with quasiperiodically moving boundaries and quasiperiodic dynamical systems (Q2574031)

The behaviour of the solution of an initial boundary value problem for a one-dimensional wave equation in a domain with time-quasiperiodically oscillating boundary is investigated. The author indicates general conditions under which every solution of the stated problem is quasiperiodic in time. One introduces and investigates the properties of the upper and lower rotation number of a quasiperiodic dynamical system, and one formulates and proves the reduction theorem of a quasiperiodic dynamical system with small perturbations. The initial boundary value problem with quasiperiodic boundary condition for homogeneous wave equation as well as the boundary value problem for nonhomogeneous wave equation are investigated.