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

Straughan, Brian

doi:10.3934/eect.2014.3.541

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

Straughan, Brian

Authors

Brian Straughan

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
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

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Copyright Statement
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Evolution equations and control theory following peer review. The definitive publisher-authenticated version Straughan, Brian (2014). Shocks and acceleration waves in modern continuum mechanics and in social systems. Evolution Equations and Control Theory 3(3): 541-555 is available online at: https://doi.org/10.3934/eect.2014.3.541