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One-Equation Local Hyperbolic Models

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Hyperbolic and Kinetic Models for Self-organised Biological Aggregations

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2232))

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Abstract

The first step in the investigation of transport models for aggregation and movement, is represented by the study of one-equation models. To emphasise the complexity of these models, we start with a variety of hyperbolic models for car traffic and pedestrian traffic (since the models for collective movement of pedestrians are a natural extension of the car traffic models, and moreover traffic-like aspects can be found in many biological systems). Next, we discuss models for animal movement that incorporate constant or linear velocity functions. We review also models with reaction terms describing the inflow/outflow of cars and populations. In the context of animal movement, we present in more detail an analytical investigation of the speed of travelling waves. We conclude with a very brief discussion of numerical approaches for advection equations.

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Authors and Affiliations

  1. Division of Mathematics, University of Dundee, Dundee, UK

    Raluca Eftimie

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  1. Raluca Eftimie
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Eftimie, R. (2018). One-Equation Local Hyperbolic Models. In: Hyperbolic and Kinetic Models for Self-organised Biological Aggregations. Lecture Notes in Mathematics(), vol 2232. Springer, Cham. https://doi.org/10.1007/978-3-030-02586-1_3

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