{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:45:19Z","timestamp":1760233519189,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T00:00:00Z","timestamp":1611187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. A suitable discrete Lyapunov function is analyzed to provide ISS of a discrete equilibrium for the proposed numerical approximation. Finally, we show computational results to validate the theoretical findings.<\/jats:p>","DOI":"10.3390\/axioms10010012","type":"journal-article","created":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T09:49:21Z","timestamp":1611222561000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Input-to-State Stability of a Scalar Conservation Law with Nonlocal Velocity"],"prefix":"10.3390","volume":"10","author":[{"given":"Simone","family":"G\u00f6ttlich","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Mannheim, 68131 Mannheim, Germany"}]},{"given":"Michael","family":"Herty","sequence":"additional","affiliation":[{"name":"IGPM, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany"}]},{"given":"Gediyon","family":"Weldegiyorgis","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1137\/040604625","article-title":"A model for the dynamics of large queuing networks and supply chains","volume":"66","author":"Armbruster","year":"2006","journal-title":"SIAM J. 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