On the attainable set for a scalar nonconvex conservation law

Boris Andreianov (1) , Carlotta Donadello (2) , Andrea Marson (3)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 Dipartimento di Matematica [Padova]

We consider a Cauchy problem for a scalar conservation law in one space dimension with a compactly supported initial datum. The flux function f is assumed to be non convex, in particular to have a single inflection point. We regard the initial datum as a control. The main result of the paper states sufficient conditions for a function v to be attained at time T by a trajectory the equation.

Mots clés: scalar conservation laws; nonconvex flux; control

Domaines: Equations aux dérivées partielles [math.AP]

Boris Andreianov, Carlotta Donadello, Andrea Marson. On the attainable set for a scalar nonconvex conservation law. 2016. ⟨hal-01346993⟩