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Shocks and acceleration waves in modern continuum mechanics and in social systems. (English) Zbl 1304.35421
Summary: 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.

MSC:
35L67 Shocks and singularities for hyperbolic equations
92F05 Other natural sciences (mathematical treatment)
92D40 Ecology
35L60 First-order nonlinear hyperbolic equations
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