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Zbl 1205.35170
Borsche, Raul; Colombo, Rinaldo M.; Garavello, Mauro
On the coupling of systems of hyperbolic conservation laws with ordinary differential equations. (English)
[J] Nonlinearity 23, No. 11, 2749-2770 (2010). ISSN 0951-7715; ISSN 1361-6544/e

Summary: 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.

MSC 2000:: *35M33
35L65 Conservation laws
34A12 Initial value problems for ODE
35L50 First order hyperbolic systems, boundary value problems
35Q92

Keywords: coupling via boundary conditions; piston problem

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