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Asymptotic stability of stationary states in wave equation coupled to nonrelativistic particle

We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. It is assumed that the charge density satisfies the Wiener condition which is a version of the "Fermi Golden Rule". We prove that in the large time approximation any finite energy solution, with the initial state close to the some stable stationary solution, is a sum of this stationary solution and a dispersive wave which is a solution of the free wave equation.

preprint2015arXivOpen access
E. KopylovaA. Komech
math-phmath.MP
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E. KopylovaA. Komech

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