Premium
Analyticity for Kuramoto–Sivashinsky‐type equations in two spatial dimensions
Author(s) -
Ioakim Xenakis,
Smyrlis YiorgosSokratis
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3631
Subject(s) - mathematics , attractor , type (biology) , infinity , variety (cybernetics) , order (exchange) , mathematical analysis , kuramoto model , function (biology) , pure mathematics , mathematical physics , synchronization (alternating current) , combinatorics , statistics , topology (electrical circuits) , biology , ecology , finance , evolutionary biology , economics
I. Stratis In this work, we investigate the analyticity properties of solutions of Kuramoto–Sivashinsky‐type equations in two spatial dimensions, with periodic initial data. In order to do this, we explore the applicability in three‐dimensional models of a spectral method, which was developed by the authors for the one‐dimensional Kuramoto–Sivashinsky equation. We introduce a criterion, which provides a sufficient condition for analyticity of a periodic function u ∈ C ∞ , involving the rate of growth of ∇ n u , in suitable norms, as n tends to infinity. This criterion allows us to establish spatial analyticity for the solutions of a variety of systems, including Topper–Kawahara, Frenkel–Indireshkumar, and Coward–Hall equations and their dispersively modified versions, once we assume that these systems possess global attractors. Copyright © 2015 John Wiley & Sons, Ltd.