Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T18:20:16.758Z Has data issue: false hasContentIssue false

Dynamics in the fundamental solution of a non-convex conservation law

Published online by Cambridge University Press:  11 December 2015

Yong-Jung Kim
Affiliation:
Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea ([email protected])
Young-Ran Lee
Affiliation:
Department of Mathematics, Sogang University, 5 Baekbeom-ro, Mapo-gu, Seoul 121-742, Republic of Korea ([email protected])

Extract

There is a huge jump in the theory of conservation laws if the convexity assumption is dropped. We study a scalar conservation law without the convexity assumption by monitoring the dynamics in the fundamental solution. We introduce three shock types in addition to the usual genuine shock: left-, right- and double-sided contacts. There are three kinds of phenomenon for these shocks, called branching, merging and transforming. All of these shocks and phenomena can be observed if the flux function has two inflection points. A comprehensive picture of a global dynamics of a non-convex flux is discussed in terms of characteristic maps and dynamical convex–concave envelopes.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)