Evolution equations arising from non-standard irreversible models

Date

Dec 20, 2017

Time

5:00 PM - 6:00 PM

Speaker

Prof. Goro Akagi

Affiliation

Tohoku University, Tohokudai, Japan

Series

TUD Dresdner Mathematisches Seminar

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. Stefan Neukamm

Description

Irreversible phenomena (e.g., diffusion, phase transition, friction) are one of most fundamental physical phenomena and also play a crucial role in our life. Therefore such irreversible phenomena have been attracting much interest of physicists and mathematicians and some classical theories have already been established in the last century. On the other hand, many irreversible phenomena beyond the classical theories were also observed, and therefore, various modified models have been also proposed. In particular, from a macroscopic point of view, various nonlinear and nonlocal PDEs have been introduced to describe such non-classical aspects of irreversible phenomena. In this talk, we shall overview several nonlinear and nonlocal evolution equations (or PDEs) which arise from non-standard irreversible models. We shall start with (relatively well-known) porous medium and fast diffusion equations, which are sorts of nonlinear diffusion equations and describe anomalous diffusion. Then several curious equations will be exhibited as generalized or related ones of these equations. They may include an infinity-Laplace parabolic equation, variable exponent cases, doubly-nonlinear equations and some limiting equations. We may also discuss evolution equations including fractional derivatives, which are recently well studied and known as an another direction to provide a description fitter for anomalous diffusion.

Last modified: Dec 1, 2017, 1:22:45 PM