Preprint 68/1998

On transitions to stationary states in 1D nonlinear wave equations

Alexander Komech

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Submission date: 23. Jan. 1999
Pages: 68
published in: Archive for rational mechanics and analysis, 149 (1999) 3, p. 213-228 
DOI number (of the published article): 10.1007/s002050050173
with the following different title: On transitions to stationary states in one-dimensional nonlinear wave equations
MSC-Numbers: 35L70, 37K40, 37K45
Keywords and phrases: attractor, stationary state, fréchet topology, energy scattering to infinity, goursat problem

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 tex2html_wrap_inline172 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'').

18.10.2019, 02:10