On the attainable set for scalar balance laws with distributed control∗
Revised: 22 December 2014
The paper deals with the set of attainable profiles of a solution u to a scalar balance law in one space dimension with strictly convex flux function
∂tu + ∂xf(u) = z(t, x).
Here the function z is regarded as a bounded measurable control. We are interested in studying the set of attainable profiles at a fixed time T > 0, both in case z(t,·) is supported in the all real line, and in case z(t,·) is supported in a compact interval [a, b] independent on the time variable t.
Mathematics Subject Classification: 35L65 / 35Q93
Key words: Conservation laws / distributed control
This research was partially supported by the UE project ERC Starting Grant CONLAWS Systems of Hyperbolic Conservation Laws: Singular Limits, Properties of Solutions and Control Problems, by the Italian Ministry of University and Research PRIN project Systems of Conservation Laws and Fluid Dynamics: Methods and Applications, and by CARIPARO Project NPDE Nonlinear Partial Differential Equations: models, analysis, and control-theoretic problems.
© EDP Sciences, SMAI 2016