SMS scnews item created by Eduardo Altmann at Tue 28 Aug 2018 1701
Type: Seminar
Distribution: World
Expiry: 25 Sep 2018
Calendar1: 5 Sep 2018 1400-1500
CalLoc1: AGR Carslaw 829
Auth: ega@dora.maths.usyd.edu.au

Applied Maths Seminar

Stability analysis of localised patterns in two and three spatial dimensions

Tzou

Wednesday September 5, 2pm in the AGR room

Dr. Justin Tzou (Macquarie University)

Title: Stability analysis of localised patterns in two and three spatial dimensions

Abstract: We present a matched asymptotics framework for constructing and analysing the stability of localised patterns that arise in singularly perturbed activator-inhibitor reaction-diffusion systems. In two spatial dimensions, by way of analyses of nonlocal eigenvalue problems, we resolve two long-standing problems regarding 1) the stability of spot patterns to oscillatory instabilities, and 2) the stability of stripe patterns to break-up instabilities, the latter motivated by the persistence of striped vegetation patterns on steep hillsides. In three spatial dimensions, we calculate explicit stability thresholds for self-replication and annihilation of spots, and derive a gradient flow that governs their slow dynamics. Joint work with Theodore Kolokolnikov, Michael J. Ward, and Shuangquan Xie.

The Webpage of the Applied Maths Seminars can be found here .


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