TL;DR
This paper systematically derives and rigorously justifies amplitude equations for Turing bifurcations in reaction-diffusion-convection systems, extending analysis to include higher-order, nonlocal, and hyperbolic systems.
Contribution
It provides a comprehensive derivation and justification of amplitude equations for Turing bifurcations in a broad class of reaction-diffusion-convection systems, including complex extensions.
Findings
Derivation of amplitude equations for Turing bifurcations.
Rigorous justification using Lyapunov-Schmidt reduction.
Extension to higher-order, nonlocal, and hyperbolic systems.
Abstract
Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically derive formally by multiscale expansion and justify rigorously by Lyapunov-Schmidt reduction amplitude equations describing Turing-type bifurcations of general reaction diffusion convection systems. Notably, our analysis includes also higher-order, nonlocal, and even certain semilinear hyperbolic systems.
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