Dynamics in the fundamental solution of a nonconvex conservation law
نویسندگان
چکیده
There is a huge jump in the theory of conservation laws if the convexity assumption is dropped. In this paper we study a scalar conservation law without the convexity assumption by monitoring the dynamics in the fundamental solution. Three extra shock types are introduced other than the usual genuine shock, which are left, right and double sided contacts. There are three kinds of phenomena of these shocks, which are 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 nonconvex flux is discussed in terms of characteristic maps and dynamical convex-concave envelopes.
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