On the analyticity of certain dissipative-dispersive systems
Papageorgiou, Demetrios T.
SourceBulletin of the London Mathematical Society
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We study the analyticity properties of solutions of dissipative-dispersive evolutionary equations possessing global attractors. We utilize an analyticity criterion for spatially periodic functions, which involves the rate of growth of the L2-norm of the nth derivative, as n tends to infinity. This criterion is applied to the dispersively modified Kuramoto-Sivashinsky equation and a general class of semilinear evolutionary pseudo-differential equations, under certain conditions, provided they possess global attractors. The proof is spectral and is fundamentally different from the semigroup approach in Collet et al. ['Analyticity for the Kuramoto-Sivashinsky equation', Physica D 67 (1993) 321-326]it utilizes an inductive method to show that the analyticity criterion holds. © 2012 London Mathematical Society.