2024/01/23 by Nicole Gauß, Anna Logioti, Gauss, Nicole +5
Computer Science · Medicine · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.2401.12660
openalex publication_date 2024/01/23 · openalex created_date 2024/01/25 · openalex updated_date 2026/07/28
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.