On the coupling of systems of hyperbolic conservation laws with ordinary differential equations
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Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples considered, numerical integrations are provided.
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Using φ(t) avoids the density-based transformation employed in prior work and feeds the predicted flux directly into (75).
“By using the ϕ ( t ) , we avoid the density-based transformation employed in prior work (e.g. [9,15,23], and instead feed the predicted flux directly into (75).”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [9]
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Li, T., Shang, P., & Diagne, M. (2026) · Automatica · doi:10.1016/j.automatica.2026.113282
- Authors
- Borsche, R., Colombo, R. M., & Garavello, M.
- Affiliations
- University of Kaiserslautern (DE)
- University of Brescia (IT)
- Università degli Studi del Piemonte Orientale “Amedeo Avogadro” (IT)
- Venue
- Nonlinearity
- Publisher
- IOP Publishing
- Published
- 2010-10-04
- Volume
- 23
- Issue
- 11
- Pages
- 2749-2770
- ISSN
- 0951-7715 (ISSN-L)
- 1361-6544
- OpenAlex
- W2080692483
- Cited by
- 55
- References
- 29
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 2 · 2023: 3 · 2022: 1 · 2021: 4 · 2020: 3 · 2019: 4 · 2018: 5 · 2017: 2 · 2016: 7 · 2015: 3 · 2014: 9 · 2013: 3 · 2012: 3
- FWCI
- 2.83
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Nonlinearity (publishedVersion)
- BOA (University of Milano-Bicocca) (submittedVersion)
- Institutional Research Information System (Università degli Studi di Brescia) (submittedVersion)
- Funders
- Deutscher Akademischer Austauschdienst
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Waves and Solitons
- Physical Sciences › Mathematics › Numerical Analysis › Differential Equations and Numerical Methods
- Keywords
- hyperbolic conservation laws, ordinary differential equations, boundary conditions, piston problem, blood flow, supply chain dynamics, numerical integration
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