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Sibirsk. Mat. Zh., 2003, Volume 44, Number 1, Pages 73–86 (Mi smj1169)  

On dissipative phenomena of the interaction of Hamiltonian systems

O. Yu. Dinariev

Schmidt United Institute of Physics of the Earth, Russian Academy of Scienses

Abstract: The dynamics is under study of a composite Hamiltonian system that is the union of a finite-dimensional nonlinear system and an infinite-dimensional linear system with quadratic interaction Hamiltonian. The dynamics of the finite-dimensional subsystem is determined by a nonlinear integro-differential equation with a relaxation kernel. We prove existence and uniqueness theorems and find a priori estimates for a solution. Under some assumptions on the form of interaction, the solution to the finite-dimensional subsystem converges to one of the critical points of the effective Hamiltonian.

Keywords: Hamiltonian, relaxation kernel, dissipative phenomena, integro-differential equation

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English version:
Siberian Mathematical Journal, 2003, 44:1, 61–72

Bibliographic databases:

UDC: 517.9
Received: 28.08.2001

Citation: O. Yu. Dinariev, “On dissipative phenomena of the interaction of Hamiltonian systems”, Sibirsk. Mat. Zh., 44:1 (2003), 73–86; Siberian Math. J., 44:1 (2003), 61–72

Citation in format AMSBIB
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\paper On dissipative phenomena of the interaction of Hamiltonian systems
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 1
\pages 73--86
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1967608}
\zmath{https://zbmath.org/?q=an:1031.37045}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 1
\pages 61--72
\crossref{https://doi.org/10.1023/A:1022012304018}
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