Global solution of the cauchy problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws

Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients

“…This complicates the analysis, and in order to prove compactness of approximated solutions a singular transformation Ψ(k, u) has been used by several authors [23,29,30,45]. In these works convergence of the Glimm scheme and of front tracking was established in the case where k may be discontinuous.…”

Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains

“…The coincidence of rarefaction and shock curves is the defining property of the Temple class [19]. The LeRoux system is a further member of this class.…”

Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities

“…In contrast, for hyperbolic equations with singular coefficients, or conservation laws with discontinuous flux functions, the convergence rate results for numerical methods are much less studied, although many authors have studied the convergence of the numerical methods. The convergence studies include the convergence of a front tracking method for conservation laws with discontinuous flux functions [4], the convergence of front tracking schemes [3,5,18,19], the Lax-Friedrichs scheme [17] and convergence rate estimates for Godunov's and Glimm's methods [21,28] for the resonant systems of conservation laws, the convergence of monotone schemes for synthetic aperture radar shape-from-shading equations with discontinuous intensities [23], the convergence of a class of finite difference schemes for the linear conservation equation and the transport equation with discontinuous coefficients [6], the convergence of a difference scheme, based on Godunov or Engquist-Osher flux, for scaler conservation laws with a discontinuous convex flux [30] and the extension to the nonconvex flux [31], the convergence of an upwind difference scheme of Engquist-Osher type for degenerate parabolic convection-diffusion equations with a discontinuous coefficient [16], the convergence of a relaxation scheme for conservation laws with a discontinuous coefficient [15], the convergence of Godunov-type methods for conservation laws with a flux function discontinuous in space [1], the convergence of upwind difference schemes of Godunov and Engquist-Osher type for a scalar conservation law with indefinite discontinuities in the flux function [22]. In the above cases, except for the resonant systems of conservation laws, convergence rates for numerical methods were not studied.…”