Exact Controllability of Scalar Conservation Laws with an Additional Control in the Context of Entropy Solutions

Vincent Perrollaz (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper, we study the exact controllability problem for nonlinear scalar con-servation laws on a compact interval, with a regular convex flux and in the framework of entropy solutions. With the boundary data and a source term depending only on the time as controls, we provide sufficient conditions for a state to be reachable in arbitrary small time. To do so we introduce a slightly modified wave-front tracking algorithm.

Mots clés: Entropy solution; conservation law; controllability

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Vincent Perrollaz. Exact Controllability of Scalar Conservation Laws with an Additional Control in the Context of Entropy Solutions. SIAM Journal on Control and Optimization, 2012, 50, pp.2025 - 2045. ⟨10.1137/110833129⟩. ⟨hal-01108950⟩