We review the relative entropy method in the context of hyperbolic and diffusive relaxation limits of entropy solutions for various hyperbolic models. The main example consists of the convergence from multidimensional compressible Euler equations with friction to the porous medium equation cite{LT12}. With small modifications, the arguments used in that case can be adapted to the study of the diffusive limit from the Euler-Poisson system with friction to the Keller-Segel system cite{LT13}. In addition, the $p$--system with friction and the system of viscoelasticity with memory are then reviewed, again in the case of diffusive limits cite{LT12}. Finally, the method of relative entropy is described for the multidimensional stress relaxation model converging to elastodynamics cite[Section 3.2]{LT06}, one of the first examples of application of the method to hyperbolic relaxation limits.

Relative entropy methods for hyperbolic and diffusive limits

LATTANZIO, CORRADO;
2014-01-01

Abstract

We review the relative entropy method in the context of hyperbolic and diffusive relaxation limits of entropy solutions for various hyperbolic models. The main example consists of the convergence from multidimensional compressible Euler equations with friction to the porous medium equation cite{LT12}. With small modifications, the arguments used in that case can be adapted to the study of the diffusive limit from the Euler-Poisson system with friction to the Keller-Segel system cite{LT13}. In addition, the $p$--system with friction and the system of viscoelasticity with memory are then reviewed, again in the case of diffusive limits cite{LT12}. Finally, the method of relative entropy is described for the multidimensional stress relaxation model converging to elastodynamics cite[Section 3.2]{LT06}, one of the first examples of application of the method to hyperbolic relaxation limits.
2014
1-60133-017-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/38015
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