Global Existence of the Equilibrium Diffusion Model in Radiative Hydrodynamics |
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Authors: | Chunjin LIN and Thierry GOUDON |
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Institution: | [1]Department of Mathematicsl College of Sciences, Hohai University, Nanjing 210098, China. [2]Project-Team SIMPAF, INRIA Lille Nord Europe Research Centre, Park Piazza, 40 Avenue Halley, F-59650 Villeneuve d'Ascq Cedex, France. |
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Abstract: | This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This
system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the
energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing
a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors
identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta
condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by
using fine energy estimates. The asymptotic decay of the solutions are also investigated. |
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Keywords: | Radiative hydrodynamics Initial value problem Equilibrium diffusion regime Energy method |
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