Atlas home || Conferences | Abstracts | about Atlas

Equadiff 2007
August 5-11, 2007
Vienna University of Technology
Vienna, Austria

Organizers
Anton Arnold, Josef Hofbauer, Christian Schmeiser, Alois Steindl, Peter Szmolyan, Gerald Teschl, Josef Teichmann

View Abstracts
Conference Homepage

A waiting time phenomenon in pattern forming systems
by
Wolf-Patrick Düll
University of Stuttgart
Coauthors: Guido Schneider (University of Stuttgart)

Abstract

In pattern forming systems, the real Ginzburg-Landau equation
UT = UXX + U - U|U|2
with complex-valued U(X, T), real-valued X and T ≥ 0 appears as a universal amplitude equation. In order to study slow modulations in time and space of slightly unstable spatially periodic solutions of the real Ginzburg-Landau equation, the porous medium equation
yt = (y2)xx
with real-valued y(x, t), x = aX, t = a3 T and a << 1 can be derived as an approximation equation describing the diffusion of the phase.
In degenerate diffusion equations like the porous medium equation, waiting time phenomena are well-known to occur. By proving estimates between the original solutions of the real Ginzburg-Landau equation and the approximations by the porous medium equation we show that such a waiting time phenomenon can also occur approximately in pattern forming systems.

AMS Classification: 35A35, 35K55, 35K65
Key words: Approximation, Ginzburg-Landau equation, nonlinear phase diffusion equation, porous medium equation, waiting time phenomenon, pattern formation

Date received: May 9, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caum-27.