English

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