Diffusive stability of convective Turing patterns

TL;DR

This paper rigorously justifies the Eckhaus stability criterion for convective Turing patterns in reaction-diffusion systems, extending the analysis to include higher-order, nonlocal, and hyperbolic systems, thus broadening the theoretical understanding of pattern stability.

Contribution

It provides a rigorous mathematical validation of the Eckhaus stability criterion for convective Turing patterns, including more complex systems beyond classical reaction-diffusion models.

Findings

Eckhaus stability criterion is rigorously justified.

Analysis includes higher-order, nonlocal, and hyperbolic systems.

Extends the theoretical framework for pattern stability.

Abstract

Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau approximation [SS, NW, WZ]. Notably, our analysis includes also higher-order, nonlocal, and even certain semilinear hyperbolic systems.