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Diffusive Relaxation Limit for Hyperbolic Systems

In: Numerical Mathematics and Advanced Applications

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  • Corrado Lattanzio

    (Università di L’Aquila, Sezione di Matematica per l’Ingegneria Dipartimento di Matematica Pura ed Applicata)

Abstract

The aim of this paper is to collect some results concerning relaxation limits of hyperbolic systems of balance laws toward parabolic equilibrium systems. More precisely, we will discuss BGK approximations for strongly parabolic systems in the case of weak solutions, by means of compensated compactness techniques. Moreover, we will study the case of a semilinear relaxation approximation to a 2×2 hyperbolic-parabolic equilibrium system, with applications to viscoelasticity, in the case of classical solutions in one and several space variables. The latter case will be used as a case study to apply the modulated energy estimates.

Suggested Citation

  • Corrado Lattanzio, 2006. "Diffusive Relaxation Limit for Hyperbolic Systems," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 396-403, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_34
    DOI: 10.1007/978-3-540-34288-5_34
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