Introduction to Recent Developments in Theory and Numerics for Conservation Laws

The importance of hyperbolic conservation laws for scientific and industrial applications has led to a growing amount of research activity in this field. A variety of physical phenomena in fluid mechanics, astrophysics, groundwa- ter flow, meteorology, reactive flow and several other areas can be effectively modeled by systems of conservation laws. In order to focus recent trends in theory and numerics in this research area and to stimulate further research in this field, we decided to organize the "International School on Theory and Numerics for Conservation Laws", which took place in FreiburgjLittenweiler, Germany, from 20 to 24 October 1997. The school was sponsored by the DFG-Graduiertenkolleg "Nichtlineare Dif- ferentialgleichungen, Modellierung, Theorie, Numerik, Visualisierung" at the University of Freiburg. It was attended by about 60 young international re- searchers. This volume contains the contributions of the five main lecturers of the school. Each article covers five hours of lectures on a specific new research area in the field of theory and numerics for conservation laws. Reviews of recent de- velopments are given, accompanied by new research results of the authors. The topics include a kinetic approach to conservation laws by Benoit Perthame, which can be used for the construction of approximate Riemann solvers for the full system of gas dynamics. Several ideas related to the stability and entropy analysis are discussed.