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Preprint 2006-022

Optimality Conditions for Solutions to Hyperbolic Balance Laws

Alberto Bressan and Wen Shen

Abstract: We study a class of optimization problems for solutions to a hyperbolic system of balance laws. The controller can affect the evolution of the system through the source terms, as well as the boundary conditions. Our main goal is to obtain necessary conditions in order that a piecewise regular solution, with finitely many shocks, be optimal. These necessary conditions are derived by constructing a family of “generalized cotangent vectors”, which can be transported backwards along a trajectory.

Available as PDF (240 Kbytes).
Alberto Bressan,
Wen Shen,
Publishing information:
To appear in: Proceedings of the Summer Research Conference: “Control Methods in PDE-Dynamical Systems”, that will be published in a Volume of the AMS Contemporary Mathematics series.
Updated 2006-09-10
Submitted by:
; 2006-06-03 and updated 2006-09-10.