On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems
Analysis of PDEs
2026-02-16 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2601.16145,
title = {On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems},
author = {Théo Belin and Guido Schneider},
journal= {arXiv preprint arXiv:2601.16145},
year = {2026}
}
Comments
21 pages, 1 figure