2018/08/30 by Lennon Ó Náraigh, Náraigh, Lennon Ó, Khang Ee Pang +1
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP
paper · pdf · doi:10.48550/arxiv.1808.10212
11 pages, 1 figure
openalex publication_date 2018/08/30 · arxiv created 2019/03/06 · arxiv updated 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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 Poincaré'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.