 Author
 Year
 1996
 Title
 Analyticity of Essentially Bounded Solutions to Semilinear Parabolic Systems and Validity of the GinzburgLandau Equation
 Journal
 SIAM Journal on Mathematical Analysis
 Volume  Issue number
 27  2
 Pages (fromto)
 424448
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

Some analytic smoothing properties of a general strongly coupled, strongly parabolic semilinear system of order $2m$ in $realnos^D times (0,T)$ with analytic entries are investigated. These properties are expressed in terms of holomorphic continuation in space and time of essentially bounded global solutions to the system. Given $0 < T' < T le infty$, it is proved that any weak, essentially bounded solution ${bold u} = (u_1,dots,u_N)$ in $realnos^Dtimes (0,T)$ possesses a bounded holomorphic continuation $bold u (x+iy,sigma + itau )$ into a region in $complexnos^Dtimescomplexnos$ defined by $(x,sigma )in realnos^Dtimes (T',T)$, $y < A'$ and $tau  < B'$, where $A'$ and $B'$ are some positive constants depending upon $T'$. The proof is based on analytic smoothing properties of a parabolic Green function combined with a contraction mapping argument in a Hardy space $H^infty$. Applications include weakly coupled semilinear systems of complex reactiondiffusion equations such as the complex GinzburgLandau equations. Special attention is given to the problem concerning the validity of the derivation of amplitude equations which describe various instability phenomena in hydrodynamics.
 URL
 go to publisher's site
 Language
 Undefined/Unknown
 Permalink
 http://hdl.handle.net/11245/1.427601
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