Quasi-linear Hyperbolic Equations Conservation Laws Single Conservation Laws The Decay of Solutions as t Tends to Infinity Hyperbolic Systems of Conservation Laws Pairs of Conservation Laws Notes… Expand

This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes. Special attention is… Expand

In Section 1 we present a general principle for associating nonlinear equations evolutions with linear operators so that the eigenvalues of the linear operator integrals of the nonlinear equation. A… Expand

Introduction. We start out from the following consequence of S. Bernstein's well known theorem on trigonometric polynomials. Let pn(z) be a polynomial of degree n for which | ^(^) | ^ 1 holds as \z\… Expand

Publisher Summary This chapter provides an overview of shock waves and entropy. It describes systems of the first order partial differential equations in conservation form: ∂ t U + ∂ X F = 0, F =… Expand

In a recent paper Zabusky has given an accurate estimate of the time interval in which solutions of the nonlinear string equation ytt = c2(1 + eyx)yxx exist. A previous numerical study of solutions… Expand