De Nitti N, Zuazua Iriondo E (2023)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2023
DOI: 10.1007/s10013-022-00598-9
Open Access Link: https://link.springer.com/article/10.1007/s10013-022-00598-9
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.
APA:
De Nitti, N., & Zuazua Iriondo, E. (2023). On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov Methods. Vietnam Journal of Mathematics. https://dx.doi.org/10.1007/s10013-022-00598-9
MLA:
De Nitti, Nicola, and Enrique Zuazua Iriondo. "On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov Methods." Vietnam Journal of Mathematics (2023).
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