Mielke, Alexander Floquet theory for, and bifurcations from spatially periodic patterns. (English) Zbl 0811.35008 Tatra Mt. Math. Publ. 4, 153-158 (1994). Summary: We consider elliptic systems of PDEs on infinite long cylindrical domains allowing applications such as travelling waves in reaction-diffusion systems of fluid flow in pipes. We develop a method for studying solutions which are close to a given solution \(u_ 0\) which is periodic with respect to the axial variable \(x\). Using spatial Floquet theory we are able to construct a spatial center manifold and to show that all orbitally close solutions can be described by an ODE. Cited in 2 Documents MSC: 35B32 Bifurcations in context of PDEs 35J60 Nonlinear elliptic equations 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:elliptic systems; infinite long cylindrical domains; spatial Floquet theory; spatial center manifold PDFBibTeX XMLCite \textit{A. Mielke}, Tatra Mt. Math. Publ. 4, 153--158 (1994; Zbl 0811.35008) Full Text: EuDML