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MiS Preprint
68/1998
On transitions to stationary states in 1D nonlinear wave equations
Alexander Komech
Abstract
We develop the theory of attractors for finite energy solutions to conservative nonlinear wave equations in a whole space. For "nondegenerate" equations the attractor coincides with the set of all finite energy stationary states. The convergence to the attractor holds as $t \to \pm \infty$ in the Fréchet topology defined by local energy seminorms. The proof of the attraction is based on the investigation of energy scattering to infinity. The results give a mathematical model of N.Bohr's transitions to quantum stationary states ("quantum jumps").
