On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods
Cargando...
Archivos
Fecha
2023-01-04
Autores
Título de la revista
ISSN de la revista
Título del volumen
Editor
Springer
Resumen
In this note, we prove a controllability result for entropy solutions of scalar conservation laws on a star-shaped graph. Using a Lyapunov-type approach, we show that, under a monotonicity assumption on the flux, if u and v are two entropy solutions corresponding to different initial data and same in-flux boundary data (at the exterior nodes of the star-shaped graph), then u ≡ v for a sufficiently large time. In order words, we can drive u to the target profile v in a sufficiently large control time by inputting the trace of v at the exterior nodes as in-flux boundary data for u. This result can also be shown to hold on tree-shaped networks by an inductive argument. We illustrate the result with some numerical simulations.
Palabras clave
Controllability
Entropy solutions
Lyapunov
Networks
Scalar conservation laws
Star-shaped graphs
Tree-shaped graphs
Entropy solutions
Lyapunov
Networks
Scalar conservation laws
Star-shaped graphs
Tree-shaped graphs
Descripción
Materias
Cita
De Nitti, N., & Zuazua, E. (2023). On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods. Vietnam Journal of Mathematics, 51(1), 71-88. https://doi.org/10.1007/S10013-022-00598-9