Seminar
Shannon entropy as a diagnostic tool for PDEs in conservation form

Hold Date 
20190416 12:00～20190416 13:00 


Place 
Lecture Room S W1C503, West Zone 1, Ito campus, Kyushu University 


Object person 



Speaker 
Philip Broadbridge (La Trobe University) 

Abstract:
After normalization, an evolving real nonnegative 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 fourthorder “diffusion” equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a selfconsistent 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 the constraint of prescribed variance, this leads to the central limit theorem.
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.
This will be a generalinterest talk, with most technical details omitted.