Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

LT2014

Relative entropy methods for hyperbolic and diffusive limits

​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
C. Lattanzio, A.E. Tzavaras
Hyperbolic Conservation Laws
2014

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.