Burgers' equation on a branching structure |
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| Institution: | 1. School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa;2. Institute of Mathematics, ?ód? University of Technology, ?ód?, Poland |
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| Abstract: | 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. |
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