MiS Preprint Repository

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MiS Preprint

On transitions to stationary states in 1D nonlinear wave equations

Alexander Komech


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").

MSC Codes:
35L70, 37K40, 37K45
attractor, stationary state, fréchet topology, energy scattering to infinity, goursat problem

Related publications

1999 Repository Open Access
Alexander Komech

On transitions to stationary states in one-dimensional nonlinear wave equations

In: Archive for rational mechanics and analysis, 149 (1999) 3, pp. 213-228