Applied and Computational Mathematics Seminar

Seminar Details

Speaker:
Khang Ee Pang
Affiliation:
University College Dublin
Title:
A mathematical framework for determining the stability of steady states of reaction-diffusion equations with periodic source terms
Time:
1.30PM Monday, 10 September 2018
Location:
SCN 1.25, O'Brien Centre for Science (North)

Abstract

We develop a mathematical framework for determining the stability of steady states of generic nonlinear reaction-diffusion equations with periodic source terms, in one spatial dimension. We formulate an a priori condition for the stability of such steady states, which relies only on the properties of the steady state itself. The mathematical framework is based on Bloch's theorem and a generalization of Poincaé's inequality for mean-zero periodic functions. Our framework can be used for stability analysis to determine the regions in an appropriate parameter space for which steady-state solutions are stable.

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