Burgers' equation on a branching structure

The initial value problem of Burgers' equation on a branching structure consisting of N semi-infinite line segments radiating from a common junction is solved in terms of a set of N linear integral equations of Volterra type involving N + 1 unknowns, coupled by a single nonlinear constraint ens...

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Bibliographic Details
Published in:Physics letters. A 1997-04, Vol.229 (1), p.37-43
Main Authors: Bressloff, P.C., Dwyer, V.M., Kearney, M.J.
Format: Article
Language:English
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Summary:The initial value problem of Burgers' equation on a branching structure consisting of N semi-infinite line segments radiating from a common junction is solved in terms of a set of N linear integral equations of Volterra type involving N + 1 unknowns, coupled by a single nonlinear constraint ensuring current conservation at the junction. We outline an iterative scheme for solving these integral equations, and illustrate their application to physical problems by considering a simple phenomenological model of road traffic.
ISSN:0375-9601
1873-2429
DOI:10.1016/S0375-9601(97)00172-2