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Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres

Стохастична динаміка як границя гамільтонової динаміки пружних куль

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Ukrainian Mathematical Journal Aims and scope

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Abstract

We consider the stochastic dynamics that is the Boltzmann-Grad limit of the Hamiltonian dynamics of a system of hard spheres. A new concept of averages over states of stochastic systems is introduced, in which the contribution of the hypersurfaces on which stochastic point particles interact is taken into account. We give a rigorous derivation of the infinitesimal operators of the semigroups of evolution operators.

Abstract

Визначена стохаатична динаміка, яка є границею Больцмана-Греда від гамільтонової динаміки системи пружних куль. Введено нову концепцію середніх від спостережуваних за станами стохастичних систем. В ньому враховуються вклади від гіперповерхонь, на яких взаємодіуть точкові стохастичні частки. Дано строге визначення інфінітезімальних операторов для півгрупи еволюційних операторів.

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Наслідок доведено

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Authors and Affiliations

  1. Politecnico di Milano, Italy

    M. Lampis

  2. Inst. Math. Nat. Acad. Sci. Ukraine, Kiev

    D. Ya. Petrina & K. D. Petrina

Authors
  1. M. Lampis
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  2. D. Ya. Petrina
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  3. K. D. Petrina
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Additional information

This work was performed during the stay May–June 1997 of D. Ya. Petrina and during the stay September–December 1997 of K. D. Petrina as visiting professors at the Politecnico di Milano, supported by the Italian Consiglio Nazionale delle Ricerche. The authors would like to thank Prof. C. Cercignani for his comments and support.

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Lampis, M., Petrina, D.Y. & Petrina, K.D. Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres. Ukr Math J 51, 614–635 (1999). https://doi.org/10.1007/BF02515237

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  • DOI: https://doi.org/10.1007/BF02515237

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