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.
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Broadbridge, P. (2014). Applications of Integrable Nonlinear Diffusion Equations in Industrial Modelling. In: Wakayama, M., et al. The Impact of Applications on Mathematics. Mathematics for Industry, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54907-9_26
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DOI: https://doi.org/10.1007/978-4-431-54907-9_26
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