The hydrodynamic limit for a system with interactions prescribed by Ginzburg-Landau type random Hamiltonian |
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Authors: | Tadahisa Funaki |
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Affiliation: | (1) Department of Mathematics, School of Science, Nagoya University, 464-01 Nagoya, Japan |
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Abstract: | Summary As a microscopic model we consider a system of interacting continuum like spin field overRd. Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scalling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time. |
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