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On the coupling of systems of hyperbolic conservation laws with ordinary differential equations. (English) Zbl 1205.35170
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:
35M33Initial-boundary value problems for systems of mixed type
35L65Conservation laws
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
35L50First order hyperbolic systems, boundary value problems
35Q92PDEs in connection with biology and other natural sciences