The nonrelativistic limit in radiation hydrodynamics: I. Weak entropy solutions for a model problem |
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Authors: | Christian Rohde Wen-An Yong |
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Affiliation: | a Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation, D-70569 Stuttgart, Pfaffenwaldring 57, Germany b Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China |
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Abstract: | This paper is concerned with a model system for radiation hydrodynamics in multiple space dimensions. The system depends singularly on the light speed c and consists of a scalar nonlinear balance law coupled via an integral-type source term to a family of radiation transport equations. We first show existence of entropy solutions to Cauchy problems of the model system in the framework of functions of bounded variation. This is done by using difference schemes and discrete ordinates. Then we establish strong convergence of the entropy solutions, indexed with c, as c goes to infinity. The limit function satisfies a scalar integro-differential equation. |
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Keywords: | Nonrelativistic limit Radiation hydrodynamics Discrete ordinates Difference scheme BV-estimate Weak-* convergence |
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