Conservation laws with discontinuous flux: a short introduction

Conservation laws with discontinuous flux have attracted recent attention both due to their numerous applications and the intriguing theoretical challenges raised by their well-posedness and numerical analysis. This introductory note states the basic problem considered in the eight contributions of this Special Issue. Three different types of applications are surveyed where these equations appear, motivated by spatially heterogeneous physical models, adjoint problems for parameter identification, and numerical methods for systems of conservation laws, respectively. Basic problems arising in the analysis of these equations are discussed, and the contributions of the Special Issue are presented.