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

Fourth Order Diffusion Equations with Increasing Entropy

 and
*
Department of Mathematics and Statistics, La Trobe University, Bundoora VIC 3086, Australia
* Author to whom correspondence should be addressed.
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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

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