Next Article in Journal
Exact Solutions in Modified Gravity Models
Next Article in Special Issue
Multivariate Multi-Scale Permutation Entropy for Complexity Analysis of Alzheimer’s Disease EEG
Previous Article in Journal / Special Issue
Minimum Mutual Information and Non-Gaussianity Through the Maximum Entropy Method: Theory and Properties
Entropy 2012, 14(7), 1127-1139; doi:10.3390/e14071127
Article

Fourth Order Diffusion Equations with Increasing Entropy

 and *
Received: 11 April 2012; in revised form: 19 June 2012 / Accepted: 19 June 2012 / Published: 25 June 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
Download PDF [130 KB, uploaded 25 June 2012]
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.

Export to BibTeX |
EndNote


MDPI and ACS Style

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

AMA Style

Tehseen N, Broadbridge P. Fourth Order Diffusion Equations with Increasing Entropy. Entropy. 2012; 14(7):1127-1139.

Chicago/Turabian Style

Tehseen, Naghmana; Broadbridge, Philip. 2012. "Fourth Order Diffusion Equations with Increasing Entropy." Entropy 14, no. 7: 1127-1139.


Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert