Please use this identifier to cite or link to this item: http://dx.doi.org/10.18419/opus-6934
|Title:||Global existence via Ginzburg-Landau formalism and pseudo- orbits of Ginzburg-Landau approximations|
|metadata.ubs.publikation.source:||Communications in mathematical physics 164 (1994), S. 157-179. URL http://projecteuclid.org/euclid.cmp/1104270714|
|Abstract:||The 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.|
|Appears in Collections:||15 Fakultätsübergreifend / Sonstige Einrichtung|
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