Relaxation dynamics, scaling limits and convergence of relaxation schemes

Abstract

Relaxation dynamics, scaling limits, and relaxation schemes are three main topics on hyperbolic relaxation problems that, remarkably, can be well understood with one model equation. The criterion that leads to desired results for the three problems is the so called sub-characteristic condition. The criterion of this nature is also pivotal in the study of general hyperbolic relaxation problems. In this article we review the recent research development in hyperbolic relaxation problems. The emphasis is on contributions associated with our own project within ANumE priority research program. We will first review some basic properties and notions for hyperbolic relaxation problems, and then focus our investigation on three main topics associated with the underlying relaxation model: relaxation dynamics, scaling limits as well as convergence theory of relaxation schemes. © 2005 Springer-Verlag Berlin Heidelberg.