A reaction-diffusion system of λ–ω type
Part I: Mathematical analysis.

Blowey, J.F.; Garvie, M.R.

Abstract

We study two coupled reaction-diffusion equations of the $\lambda$–$\omega$ type [11] in $d\,{\le}\,3$ space dimensions, on a convex bounded domain with a $C^2$ boundary. The equations are close to a supercritical Hopf bifurcation in the reaction kinetics and are model equations for oscillatory reaction-diffusion equations. Global existence, uniqueness and continuous dependence on initial data of strong and weak solutions are proved using the classical Faedo-Galerkin method of Lions [15] and compactness arguments. We also present a complete case study for the application of this method to systems of nonlinear reaction-diffusion equations.

Citation

Blowey, J., & Garvie, M. (2005). Part I: Mathematical analysis. European Journal of Applied Mathematics, 16(1), 1-19. https://doi.org/10.1017/s0956792504005534

• Journal Article Type: Article
• Publication Date: 2005-02
• Journal: European Journal of Applied Mathematics
• Print ISSN: 0956-7925
• Electronic ISSN: 1469-4425
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 1
• Pages: 1-19
• DOI: https://doi.org/10.1017/s0956792504005534