Weak and Classical Solutions for a Model Problem in Radiation Hydrodynamics

C. Rohde (), N. Tiemann () and W. -A. Yong ()
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C. Rohde: Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation
N. Tiemann: Universität Bielefeld, Fakultät für Mathematik
W. -A. Yong: Tsinghua University, Zhou Pei-Yuan Center for Applied Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 891-899 from Springer

Abstract: It has been observed for a long time that radiation effects can prevent the development of singularities of shock-wave type in solutions for mathematical models for compressible flows. We consider a multidimensional model problem in the form of a system of nonlinear hyperbolic balance laws and prove that the associated Cauchy problem can have smooth global solutions provided that the initial data are sufficiently close to an equilibrium state. Numerical experiments confirm this result but also show that shock waves can develop for large amplitude initial data.

Keywords: Shock Wave; Cauchy Problem; Model Problem; Entropy Solution; Nonrelativistic Limit (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_93

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DOI: 10.1007/978-3-540-75712-2_93

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