ON STABILIZATION OF STRING NONLINEAR OSCILLATOR INTERACTION

In the present paper, we consider a system of equations that describes the interaction of a nonlinear oscillator with an infinite string. Th e main result is the stabilization: roughly speaking, each finite ener gy solution to the system tends to a stationary solution as t --> +inf inity (and similarly as t--> -infinity). The proof uses the descriptio n of a reversible system by an irreversible. The limit stationary solu tions corresponding to t = +/-infinity may be different and arbitrary. The result gives a mathematical model of transitions to stationary st ates in reversible systems; these transitions are similar to Bohr ones . Such transitions are impossible for finite-dimensional Hamiltonian s ystems and for linear autonomous Shrodinger equations. The paper conta ins the complete exposition and an extension of the author's recent re sults. (C) 1995 Academic Press, Inc.