Dynamics in the fundamental solution of a non-convex conservation law (Q2799615)

The authors study a scalar conservation law \(\partial_t u+\partial_x f(u)=0\) with one space variable. The flux function \(f(u)\) is supposed to have finite number of inflection points and to satisfy the super-linear growth condition at infinity. The authors prove existence and uniqueness of the fundamental entropy solution \(u(x,t)\), which satisfies the initial condition \(u(x,0)=\delta(x)\), and describe its dynamics, in terms of characteristic maps and dynamical convex-concave envelopes.