Dynamics in the fundamental solution of a non-convex conservation law. Issue 1 (February 2016)

• Record Type: Journal Article
• Authors: Kim, Yong-Jung; Lee, Young-Ran
• Is Part Of: Proceedings. Volume 146:Issue 1(2016)
• Page Start: 169
• Page End: 193
• Publication Date: 2016-02
• Subjects: convex-concave envelope, -- entropy admissibility condition, -- contact shock, -- shock dynamics; Primary 35L65, -- Secondary 76L05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000359
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : 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.