On Asymptotic Completeness of Scattering in the Nonlinear Lamb System, II

Abstract

We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point using the Inverse Function Theorem in a Banach space. We give the counterexamples showing nonexistence of such trajectories for nonhyperbolic stationary points.

References in corpus (1)

• Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit

Cited by in corpus (2)

• Attractors of Hamilton nonlinear partial differential equations
• Attractors of nonlinear Hamiltonian PDEs