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
Diffusive relaxation limit for hyperbolic systems
LATTANZIO, CORRADO
2006-01-01
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 estimatesFile in questo prodotto:
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