**Friday, 11:00 - 11:25 h, Room: H 0111**

**Sebastian Pfaff**

Optimal boundary control for nonlinear hyperbolic conservation laws with source terms

**Coauthor: Stefan Ulbrich**

**Abstract:**

Hyperbolic conservation laws arise in many different applications such as traffic modelling or fluid mechanics. The difficulty in the optimal control of hyperbolic conservation laws stems from the occurrence of moving discontinuities (shocks) in the entropy solution. This leads to the fact that the control-to-state mapping is not differentiable in the usual sense.

In this talk we consider the optimal control of a scalar balance law on a bounded spatial domain with controls in source term, initial data and the boundary condition. We show that the state depends shift-differentiably on the control by extending previous results for the control of Cauchy problems. Furthermore we present an adjoint-based gradient representation for cost functionals. The adjoint equation is a linear transport equation with discontinuous coefficients on a bounded domain which requires a proper extension of the notion of a reversible solution. The presented results form the basis for the consideration of optimal control problems for switched networks of nonlinear conservation laws.

Talk 2 of the contributed session Fri.1.H 0111

**"Optimal control of PDEs with advection terms"** [...]

Cluster 19

**"PDE-constrained optimization & multi-level/multi-grid methods"** [...]