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Weak and Classical Solutions for a Model Problem in Radiation Hydrodynamics

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • C. Rohde & N. Tiemann & W. -A. Yong, 2008. "Weak and Classical Solutions for a Model Problem in Radiation Hydrodynamics," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 891-899, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_93
    DOI: 10.1007/978-3-540-75712-2_93
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