DISSIPATION AND THE INFORMATION CONTENT OF THE DEVIATION FROM HAMILTONIAN DYNAMICS-Reference-Cited by-同舟云学术

DISSIPATION AND THE INFORMATION CONTENT OF THE DEVIATION FROM HAMILTONIAN DYNAMICS

Published:2023 Issue:1-2 Volume:15 Page:366-382
ISSN:2066-5997
Container-title:Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application
language:
Short-container-title:AnnalsARSciMath

Author:

Buliga M.,

Abstract

"We explain a dissipative version of hamiltonian mechanics, based on the information content of the deviation from hamiltonian dynam¬ics. From this formulation we deduce minimal dissipation principles, dynamical inclusions, or constrained evolution with hamiltonian drift reformulations. Among applications we recover a dynamics generaliza¬tion of Mielke et al quasistatic rate-independent processes. This article gives a clear and unitary presentation of the theory of hamiltonian inclusions with convex dissipation or symplectic Brezis- Ekeland-Nayroles principle, presented under various conventions first in [3] arXiv:0810.1419, then in [4] arXiv:1408.3102 and, for the ap¬pearance of bipotentials in relation to the symplectic duality, in [2] arXiv:1902.04598v1."

Publisher

Academia Oamenilor de Stiinta din Romania

Subject

General Mathematics

Reference14 articles.

1. [1] H. Brezis and I. Ekeland, Un principe variationnel associe a certaines equations paraboliques. I. Le cas independant du temps, II. Le cas dependant du temps. C. R. Acad. Sci. Paris Serie A-B, 282, 971-974, and 1197-1198, 1976.

2. [2] M. Buliga, On the information content of the difference from hamiltonian evolution, (2019), arXiv:1902.04598v1.

3. [3] M. Buliga, Hamiltonian inclusions with convex dissipation with a view towards applications, Mathematics and its Applications 1, 2 (2009), 228-251, arXiv:0810.1419.

4. [4] M. Buliga, G. de Saxce, A symplectic Brezis-Ekeland-Nayroles principle, Mathematics and Mechanics of Solids 22, 6, (2017) arXiv:1408.3102

5. [5] M. Buliga, A stochastic version and a Liouville theorem for hamiltonian inclusions with convex dissipation, arXiv:1807.10480