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arXiv · 2601.16145

On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems

Théo Belin·Guido Schneider
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Abstract

We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such systems and relies on key maximal regularity results. The theorem is applied to the Gray-Scott-Klausmeier vegetation-water interaction model and its application to general reaction-diffusion-advection systems is discussed.

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Théo Belin, Guido Schneider. 2026-01-22. On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems. https://arxiv.org/abs/2601.16145

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