Accession Number:

ADA160981

Title:

Sup-Norm Estimates in Glimm's Method.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1985-08-01

Pagination or Media Count:

10.0

Abstract:

A system of two conservation laws in one dimension is a set of first order nonlinear partial differential equations of a certain form 1 where u,v is a vector function of x,t, x epsilon R, t or 0. The Cauchy problem asks for a solution of 1 given the initial values of u and v at time t 0. Equations of type 1 arise, for example, in gas dynamics where they express the conservation of quantities like mass, momentum and energy, when diffusion is neglected. Typically, smooth solutions of 1 cannot be found. This is due to the formation of shock waves. Shock waves are the mechanism by which entropy is dissipated in solutions of 1. This paper gives a proof that solutions exist even after shock waves form, so long as the amplitude of the waves are not too great initially. Keywords Riemann invariants Conservation laws Stability.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE