Applications of Integrable Nonlinear Diffusion Equations in Industrial Modelling

Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)

Abstract

There are useful integrable nonlinear diffusion equations that can be transformed directly to linear partial differential equations. The possibility of linearisation allows us to incorporate a much broader class of boundary conditions than would be available under reduction by a one-parameter Lie symmetry. By this means we can solve nonlinear boundary value problems of practical significance. Examples are given in the solidification of multi-phase materials with nonlinear thermal transport coefficients, infiltration of water in unsaturated soil and evolution of a metal surface by fourth-order curvature-driven diffusion. From this approach, there arise some open mathematical problems.

Keywords

Nonlinear diffusion Stefan problems Steel solidification Unsaturated flow Infiltration Surface diffusion Grain boundaries Integrable models 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityMelbourneAustralia

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