Global existence for long wave Hopf unstable spatially extended systems with a conservation law
Analysis of PDEs
2024-01-24 v1 Dynamical Systems
Abstract
We are interested in reaction-diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number . With the help of a multiple scaling perturbation ansatz a Ginzburg-Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction-diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions.
Keywords
Cite
@article{arxiv.2401.12660,
title = {Global existence for long wave Hopf unstable spatially extended systems with a conservation law},
author = {Nicole Gauss and Anna Logioti and Guido Schneider and Dominik Zimmermann},
journal= {arXiv preprint arXiv:2401.12660},
year = {2024}
}