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This article is cited in 1 scientific paper (total in 1 paper)
Application of relaxation schemes in the microscopic theory of hydrodynamics
József Fritz Institute of Mathematics, Budapest University of Technology and Economics, Budapest
Abstract:
We consider stochastic evolution of particles moving on $\mathbb Z$ with opposite speeds. This model of interacting exclusions admits a hyperbolic (Euler) scaling, and its hydrodynamic limit results in the Leroux system of PDE theory. The basic model can be modified by introducing a spin-flip, or a creation-annihilation mechanism. In a regime of shock waves the method of compensated compactness is applied. We are going to discuss usefulness of another tool of the theory of conservation laws, the technique of relaxation schemes is extended to microscopic systems.
Key words and phrases:
interacting exclusions, hyperbolic scaling, Lax entropy pairs, compensated compactness, logarithmic Sobolev inequalities, relaxation schemes.
Received: February 7, 2010; in revised form May 8, 2010
Citation:
József Fritz, “Application of relaxation schemes in the microscopic theory of hydrodynamics”, Mosc. Math. J., 10:4 (2010), 729–745
Linking options:
https://www.mathnet.ru/eng/mmj401 https://www.mathnet.ru/eng/mmj/v10/i4/p729
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Abstract page: | 179 | References: | 47 |
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