Shocks and acceleration waves in modern continuum mechanics and in social systems

Straughan, Brian

Abstract

The use of discontinuity surface propagation (e.g. shock waves and acceleration waves) is well known in modern continuum mechanics and yields a very useful means to obtain important information about a fully nonlinear theory with no approximation whatsoever. A brief review of some of the recent uses of such discontinuity surfaces is given and then we mention modelling of some social problems where the same mathematical techniques may be used to great effect. We specifically show how to develop and analyse models for evolution of one language overtaking use of another leading to possible extinction of the former language. Then we analyse shock transmission in a model for the evolutionary transition from the human period when hunter-gatherers transformed into farming. Finally we address modelling discontinuity waves in the context of diffusion of an innovation.

Citation

Straughan, B. (2014). Shocks and acceleration waves in modern continuum mechanics and in social systems. Evolution Equations and Control Theory, 3(3), 541-555. https://doi.org/10.3934/eect.2014.3.541

• Journal Article Type: Article
• Online Publication Date: Sep 30, 2014
• Publication Date: Sep 30, 2014
• Deposit Date: Dec 6, 2018
• Publicly Available Date: Dec 6, 2018
• Journal: Evolution Equations and Control Theory
• Electronic ISSN: 2163-2480
• Publisher: American Institute of Mathematical Sciences (AIMS)
• Peer Reviewed: Peer Reviewed
• Volume: 3
• Issue: 3
• Pages: 541-555
• DOI: https://doi.org/10.3934/eect.2014.3.541
• Public URL: https://durham-repository.worktribe.com/output/1341543