We consider two physically and mathematically distinct regularization mechanisms of scalar
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …

Partial differential equations are a many-faceted subject. Created to describe the
mechanical behavior of objects such as vibrating strings and blowing winds, it has …

We study a class of coupled hyperbolic systems of conservation laws which contain the one-
dimensional zero-pressure gas dynamics as a prototypical example. The Riemann problems …

A new class of fundamental waves arises in conservation laws that are not strictly
hyperbolic. These waves serve as transitions between wave groups associated with …

S "V Page 1 SIAM J. MATH. ANAL. Vol. 19, No. 3, May 1988 1988 Society for Industrial and
Applied Mathematics 004 THE SOLUTION OF THE RIEMANN PROBLEM FOR A HYPERBOLIC …

These notes are primarily concerned with the numerical solution to hyperbolic systems of
conservation laws that arise in astrophysical calculations, primarily in" gas dynamic" …

Some recent developments in the study of the Cauchy problem for the Euler equations for
compressible fluids are reviewed. The local and global well-posedness for smooth solutions …

In immiscible three-phase flow, the lead oil bank can split into two, a Buckley-Leverett shock
wave followed by a new type of shock wave. Such a nonclassical" transitional" shock wave …

st +f(s, Cl, (1.1) Page 1 SIAM J. MATH. ANAL. Vol. 20, No. pp. 908-929, July 1989 1989
Society for Industrial and Applied Mathematics 008 THE RIEMANN PROBLEM FOR …

We introduce a unifying framework for treating all of the fundamental waves occurring in
general systems of n conservation laws. Fundamental waves are represented as pairs of …