Jordan – Cattaneo waves: Analogues of compressible flow

Straughan, B.

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.

Citation

Straughan, B. (2020). Jordan – Cattaneo waves: Analogues of compressible flow. Wave Motion, 98, Article 102637. https://doi.org/10.1016/j.wavemoti.2020.102637

• Journal Article Type: Article
• Acceptance Date: Jul 9, 2020
• Online Publication Date: Jul 24, 2020
• Publication Date: 2020-11
• Deposit Date: Jul 24, 2020
• Publicly Available Date: Jul 24, 2021
• Journal: Wave Motion
• Print ISSN: 0165-2125
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 98
• Article Number: 102637
• DOI: https://doi.org/10.1016/j.wavemoti.2020.102637