Decay with a rate for noncompactly supported solutions of conservation laws

Decay of Entropy Solutions of Nonlinear Conservation Laws 32

Fundamental Solutions of Conservation Laws

In this paper we construct fundamental solutions of a scalar conservation law in one space dimension. These source-type solutions are well known for a convex case and hence our focus is on a general non-convex case which may have a finite number of inflection points. Signed fundamental solutions are constructed first and then under an extra hypothesis on nonnegativity of the flux two parameter ...

Decay rate for perturbations of stationary discrete shocks for convex scalar conservation laws

This paper is to study the decay rate for perturbations of stationary discrete shocks for the Lax-Friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method. If the summation of the initial perturbation over (−∞, j) is small and decays at the algebraic rate as |j| → ∞, then the solution approaches the stationary discrete shock profiles at the c...

Approximate Solutions of Nonlinear Conservation Laws

This is a summary of ve lectures delivered at the CIME course on "Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" held in Cetraro, Italy, on June 1997. Following the introductory lecture I | which provides a general overview of approximate solution to nonlinear conservation laws, the remaining lectures deal with the speciics of four complementing topics: Lecture II. Finite-d...

DECAY OF ENTROPY SOLUTIONS OF NONLINEAR CONSERVATION LAWS GUI-QIANG CHEN & HERMANO FRID Dedicated to

We are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws. The main objective of this paper is to present an analytical approach and to explore its applications to studying the large-time behavior of periodic entropy solutions of hyperbolic conservation laws. The asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an import...