Decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws (Memoirs of the American Mathematical Society.)

This paper studies coupled systems of nonlinear conservation equations. The paper is divided into five long and rather difficult sections. The authors provide an instructive preface at the beginning which must be read before one attempts the main body. The major contribution in this paper is the observation that interaction of waves usually causes some cancellation of waves. Thus, the non-linearity of the characteristic speeds causes shocks and rarefaction waves of the same family to interact with each other and thereby to cancel each other out. This qualitative observation must be made quantitative, and this is done in Section 4