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Jordan – Cattaneo waves : analogues of compressible flow.

Straughan, B. (2020) 'Jordan – Cattaneo waves : analogues of compressible flow.', Wave motion., 98 . p. 102637.

Abstract

We review work of Jordan on a hyperbolic variant of the Fisher - KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee – Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible - infected (SI) model, and generalizations of diffusive Lotka – Volterra equations, including a Lotka – Volterra – Bass competition model with diffusion. For all cases we show how a Jordan - Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo – Christov poroacoustic model.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.wavemoti.2020.102637
Publisher statement:© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:09 July 2020
Date deposited:24 July 2020
Date of first online publication:24 July 2020
Date first made open access:24 July 2021

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