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Global existence of the equilibrium diffusion model in radiative hydrodynamics

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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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Author information

Correspondence to Chunjin Lin.

Additional information

Project supported by the Fundamental Research Funds for the Central Universities (No. 2009B27514) and the National Natural Science Foundation of China (No. 10871059).

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Lin, C., Goudon, T. Global existence of the equilibrium diffusion model in radiative hydrodynamics. Chin. Ann. Math. Ser. B 32, 549–568 (2011). https://doi.org/10.1007/s11401-011-0658-z

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Keywords

  • Radiative hydrodynamics
  • Initial value problem
  • Equilibrium diffusion regime
  • Energy method

2000 MR Subject Classification

  • 76N10
  • 35L65
  • 35L45
  • 35Q80