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An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity

Published online by Cambridge University Press:  17 February 2009

Peter Tritscher
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Abstract

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Members of an hierarchy of integrable nonlinear evolution equations, related to the well-known linearizable diffusion equation which has the diffusivity form as the reciprocal of the square of the concentration, are adapted to derive a new integrable nonlinear equation which models the surface evolution of an arbitrarily-oriented theoretical anisotropic material by the concomitant action of evaporation-condensation and surface diffusion. The constitutive relations are explicitly formulated and these show that the theoretical anisotropic material behaves like a liquid crystal. The integrable nonlinear equation may be used to advantage as test cases for numerical schemes. Its form has many attributes of the nonlinear governing equation for an isotropic material. Closed-form solutions are constructed for the evolution of a ramped surface by concomitant evaporation-condensation and surface diffusion.

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Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 4 , April 1997, pp. 518 - 541
Copyright
Copyright © Australian Mathematical Society 1997

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