2026/07/17 by Annalisa Iuorio, Cinzia Soresina, Frits Veerman
#math.DS #nlin.PS
Using geometric singular perturbation theory, we construct stationary, periodic, front-type far-from-equilibrium patterns in a cross-diffusion model for plant growth under the influence of toxicity. We show how existing techniques for the analysis of far-from-equilibrium patterns in one spatial dimension can be extended to include cross-diffusion terms and prove the existence of a one-parameter family of these patterns. For a general cross-diffusion model class, we show when front-type patterns may appear depending on the shape of the critical manifold, which is determined by the specific properties of the reaction terms.