NOTE ON SHOCKS IN NONLINEAR SIMILARITY FIELDS.

Nima Geffen*, Levi Lustman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Similarity analysis has been most helpful in treating nonlinear heat conduction, boundary layers, explosions and plasmadynamic problems. Whenever the nonlinear system is of a hyperbolic type, as is the case in all nonlinear wave propagations (in solids, liquids, gases and plasmas), or mixed, e. g. transonic or transcritical fluidynamic flows, shocks may be present in the field. The question then arises, whether these shocks will comply with the similarity assumption, and will occur along similarity lines across which the correct jump conditions will be expressible in terms of similarity variables only. In this article similarity shocks are derived for a system of two quasi-linear, first order partial differential equations, a necessary and sufficient condition for such shocks to exist is given and a few gasdynamic examples shown.

Original languageEnglish
Pages (from-to)397-441
Number of pages45
JournalIndiana University Mathematics Journal
Volume25
Issue number5
DOIs
StatePublished - 1976

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