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A Ginzburg-Landau approximation theorem for quasilinear pattern-forming systems in uniformly local Sobolev spaces
Théo Belin, Guido Schneider
We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear or fully nonlinear pattern-forming systems close to the first instability. We present an a…
On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems
Théo Belin, Guido Schneider
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 p…
Some remarks about an effective description of high-frequency wave-packet propagation
Anna Logioti, Xin Meng, Guido Schneider
We consider systems of the form $ \partial_τ \mathcal U + \mathcal A(\partial_ξ) \mathcal U + \frac{1}{\varepsilon} \mathcal E \mathcal U = \mathcal T_{2}( \mathcal U , \mathcal U…
Global existence for long wave Hopf unstable spatially extended systems with a conservation law
Nicole Gauss, Anna Logioti, Guido Schneider +1
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 pert…