Schneider, Guido2009-06-302016-03-312009-06-302016-03-311994309021472http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-40771http://elib.uni-stuttgart.de/handle/11682/6951http://dx.doi.org/10.18419/opus-6934The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the cubic term of the formally derived Ginzburg-Landau equation has negative real part the method allows to show global existence in time in the original system of all solutions belonging to small initial conditions in L∞. Another aim of this paper is to construct a pseudo-orbit of Ginzburg-Landau approximations which is close to a solution of the original system up to t = ∞. We consider here as an example the socalled Kuramoto-Shivashinsky equation to explain the methods, but it applies also to a wide class of other problems, like e.g. hydrodynamical problems or reaction-diffusion equations, too.eninfo:eu-repo/semantics/openAccessGinzburg-Landau-Gleichung , Ginzburg-Landau-Theorie510article2014-10-16