Traveling wave dynamics for Allen-Cahn equations with non-decreasing constraint

Datum

04.07.2019

Zeit

15:15 - 16:15

Sprecher

Prof. Goro Akagi

Zugehörigkeit

Tohoku University, Mathematical Institute (Sendai, Japan)

Serie

TUD Mathematik Oberseminar Analysis

Sprache

en

Hauptthema

Mathematik

Host

Prof. Dr. St. Neukamm

Beschreibung

This talk concerns a one-dimensional Allen-Cahn equation on the whole line with non-decreasing constraint, which forces the growth of each solution to be non-decreasing. The study on such constrained evolution equations are motivated from phase-field models in Damage Mechanics. Indeed, evolution of damage is supposed to be monotone due to the nature of damaging. In this talk, we shall discuss traveling wave dynamics, which has been well studied for classical Allen-Cahn equations, for the constrained one. More precisely, we shall start with constructing a traveling wave solution and investigate its properties. Furthermore, the traveling wave dynamics turns out to be relevant to a free boundary problem with a peculiar motion equation for the boundary through an analysis on a regularity issue for the constrained Allen-Cahn equation, and then, such a viewpoint brings us a perspective on a stability issue for traveling waves.

Oberseminar Analysis

Letztmalig verändert: 18.06.2019, 11:58:06