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Geometric Analysis and Partial Differential Equations Seminar

February 28, 2013 @ 10:30 am - 11:30 pm

Geometric Analysis and Partial Differential Equations Seminar Series at UOW
Speaker

Prof. Philip Broadbridge (La Trobe University)

Title

Shannon entropy as a diagnostic tool for PDEs in conservation form

Abstract

After normalization, an evolving real non-negative function may be viewed as a probability density. From this we may derive the corresponding evolution law for Shannon entropy. Parabolic equations, hyperbolic equations and fourth-order “diffusion” equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a self-consistent manner and at an elementary level by reference to some simple evolution equations such as the linear heat equation. It is easily seen that the 2nd law of thermodynamics is equivalent to loss of Shannon information when temperature obeys a general nonlinear 2nd order diffusion equation. With fourth order diffusion terms, new problems arise. We know from applications such as thin film flow and surface diffusion, that fourth order diffusion terms may generate ripples and they do not satisfy the Second Law. Despite this, we can identify the class of fourth order quasilinear diffusion equations that increase the Shannon entropy.

Details

Date:
February 28, 2013
Time:
10:30 am - 11:30 pm
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Venue

Building 39C Room 174
University of Wollongong
Wollongong, 2500
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