Relative entropy methods for hyperbolic and diffusive limits

Bibliography:

C. Lattanzio, A.E. Tzavaras, Relative entropy methods for hyperbolic and diffusive limits, In Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona, A. Bressan, P. Marcati, A. Marson, eds; AIMS Series on Applied Mathematics, Vol 8, Springfield, 2014, pp. 163-177

Authors:

C. Lattanzio, A.E. Tzavaras

Keywords:

Hyperbolic Conservation Laws

Year:

2014

Abstract:

Abstract

We review the relative entropy method in the context of hyper-
bolic 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 [7].
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 [8]. In addition, the p–system with friction and the
system of viscoelasticity with memory are then reviewed, again in the case of
diffusive limits [7]. Finally, the method of relative entropy is described for the
multidimensional stress relaxation model converging to elastodynamics [6, Sec-
tion 3.2], one of the first examples of application of the method to hyperbolic
relaxation limits.

Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

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