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

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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.
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2016-02
Language
English
Article Type
Article
Keywords

ASYMPTOTIC-BEHAVIOR; CONVEXITY CONDITIONS; CONVERGENCE; REGULARITY

Citation

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v.146, no.1, pp.169 - 193

ISSN
0308-2105
DOI
10.1017/S0308210515000359
URI
http://hdl.handle.net/10203/207957
Appears in Collection
MA-Journal Papers(저널논문)
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