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Analyticity for a class of non-linear evolutionary pseudo-differential equations

Published online by Cambridge University Press:  02 September 2014

XENAKIS IOAKIM  and
YIORGOS-SOKRATIS SMYRLIS
XENAKIS IOAKIM
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus emails: xioaki01@ucy.ac.cy, smyrlis@ucy.ac.cy
YIORGOS-SOKRATIS SMYRLIS
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus emails: xioaki01@ucy.ac.cy, smyrlis@ucy.ac.cy
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Abstract

We study the analyticity properties of solutions for a class of non-linear evolutionary pseudo-differential equations possessing global attractors. In order to do this we utilise an analyticity criterion for spatially periodic functions, which involves the rate of growth of a suitable norm of the nth derivative of the solution, with respect to the spatial variable, as n tends to infinity. This criterion can be used to a wide class of dissipative-dispersive partial differential equations, provided they possess global attractors. Using this criterion and the spectral method developed in Akrivis et al. [1] we have improved previous results.

Keywords

Kuramoto-Sivashinksy equationDissipative-dispersive equationsAnalyticity of solutions of partial differential equationsGlobal attractors

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 6 , December 2014 , pp. 783 - 793
Copyright
Copyright © Cambridge University Press 2014 

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