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@article{Papageorgiou:2022:imamat/hxac028,
author = {Papageorgiou, DT and Smyrlis, Y-S and Tomlin, RJ},
doi = {imamat/hxac028},
journal = {IMA Journal of Applied Mathematics},
pages = {964--984},
title = {Optimal analyticity estimates for non-linear active-dissipative evolution equations},
url = {http://dx.doi.org/10.1093/imamat/hxac028},
volume = {87},
year = {2022}
}

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TY  - JOUR
AB  - Active–dissipative evolution equations emerge in a variety of physical and technological applications including liquid film flows, flame propagation, epitaxial film growth in materials manufacturing, to mention a few. They are characterized by three main ingredients: a term producing growth (active), a term providing damping at short length scales (dissipative) and a nonlinear term that transfers energy between modes and crucially produces a nonlinear saturation. The manifestation of these three mechanisms can produce large-time spatiotemporal chaos as evidenced by the Kuramoto-Sivashinsky equation (negative diffusion, fourth-order dissipation and a Burgers nonlinearity), which is arguably the simplest partial differential equation to produce chaos. The exact form of the terms (and in particular their Fourier symbol) determines the type of attractors that the equations possess. The present study considers the spatial analyticity of solutions under the assumption that the equations possess a global attractor. In particular, we investigate the spatial analyticity of solutions of a class of one-dimensional evolutionary pseudo-differential equations with Burgers nonlinearity, which are periodic in space, thus generalizing the Kuramoto-Sivashinsky equation motivated by both applications and their fundamental mathematical properties. Analyticity is examined by utilizing a criterion involving the rate of growth of suitable norms of the nth spatial derivative of the solution, with respect to the spatial variable, as n tends to infinity. An estimate of the rate of growth of the nth spatial derivative is obtained by fine-tuning the spectral method, developed elsewhere. We prove that the solutions are analytic if γ, the order of dissipation of the pseudo-differential operator, is higher than one. We also present numerical evidence suggesting that this is optimal, i.e. if γ is not larger that one, then the solution is not in general analytic. Extensive numeri
AU  - Papageorgiou,DT
AU  - Smyrlis,Y-S
AU  - Tomlin,RJ
DO  - imamat/hxac028
EP  - 984
PY  - 2022///
SN  - 0272-4960
SP  - 964
TI  - Optimal analyticity estimates for non-linear active-dissipative evolution equations
T2  - IMA Journal of Applied Mathematics
UR  - http://dx.doi.org/10.1093/imamat/hxac028
UR  - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000885725400001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
UR  - https://academic.oup.com/imamat/article/87/6/964/6760949
UR  - http://hdl.handle.net/10044/1/103988
VL  - 87
ER  -

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