In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

Some aspects of recent developments in the study of the Euler equations for compressible fluids and related hyperbolic conservation laws are analyzed and surveyed. Basic features and phenomena including convex entropy, symmetrization, hyperbolicity, genuine nonlinearity, singularities, BV bound, concentration, and cavitation are exhibited. Global well-posedness for discontinuous solutions, incl...

Abstract of the meeting is here. Mathematics Subject Classification (2000): AMS-CLASSIFICATION. Introduction by the Organisers This meeting was well attended with over 30 participants with broad geographic representation from all continents. This workshop was a nice blend of researchers with various backgrounds . . . Hyperbolic Conservation Laws 3 Workshop: Hyperbolic Conservation Laws Table of

Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...

Compared to standard numerical methods for hyperbolic systems of conservation laws, Kinetic Schemes model propagation of information by particles instead of waves. In this article, the wave and the particle concept are shown to be closely related. Moreover, a general approach to the construction of Kinetic Schemes for hyperbolic conservation laws is given which summarizes several approaches dis...

Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions. 1-Review of basic theory. This chapter...

This paper concerns the asymptotic behavior toward rarefaction waves of the solution of a genera) 2 x 2 hyperbolic conservation laws with positive viscosity. We prove that if the initial data is close to a constant state and its values at + a3 lie on the kth rarefaction curve for the corresponding hyperbolic conservation laws, then the solution tends as I + co to the rarefaction wave determined...