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Entropy 2012, 14(7), 1127-1139; doi:10.3390/e14071127

Fourth Order Diffusion Equations with Increasing Entropy

Department of Mathematics and Statistics, La Trobe University, Bundoora VIC 3086, Australia
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Received: 11 April 2012 / Revised: 19 June 2012 / Accepted: 19 June 2012 / Published: 25 June 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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Abstract

The general quasi-linear autonomous fourth order diffusion equation ut = −[G(u)uxxx + h(u, ux, uxx)]x with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general class of equations for which the Shannon entropy density obeys a reaction-diffusion equation with a positive irreducible source term. Such equations may have any positive twice-differentiable diffusivity function G(u). The forms of such equations are the indicators of more general conservation equations whose entropy equation may be expressed in an alternative reaction-diffusion form whose source term, although reducible, is positive.
Keywords: Shannon entropy; fourth order diffusion; irreversibility Shannon entropy; fourth order diffusion; irreversibility
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Tehseen, N.; Broadbridge, P. Fourth Order Diffusion Equations with Increasing Entropy. Entropy 2012, 14, 1127-1139.

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