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arXiv · 2401.12660

Global existence for long wave Hopf unstable spatially extended systems with a conservation law

Nicole Gauss·Anna Logioti·Guido Schneider·Dominik Zimmermann
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Abstract

We are interested in reaction-diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number $k = 0$. 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.

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Nicole Gauss, Anna Logioti, Guido Schneider, Dominik Zimmermann. 2024-01-23. Global existence for long wave Hopf unstable spatially extended systems with a conservation law. https://arxiv.org/abs/2401.12660

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