# The impact of advection on large-wavelength stability of stripes near planar Turing instabilities

@article{Yang2019TheIO, title={The impact of advection on large-wavelength stability of stripes near planar Turing instabilities}, author={Jichen Yang and J. Rademacher and E. Siero}, journal={arXiv: Analysis of PDEs}, year={2019} }

It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of weak anisotropy by directional advection on such solutions, and the role of quadratic terms. We focus on the generic form of planar reaction-diffusion systems with two components near such a bifurcation. Using Lyapunov-Schmidt reduction and Floquet-Bloch decomposition we derive a rigorous parameter expansion for… Expand

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