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A priori bounds for rough differential equations with a non-linear damping term

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Title: A priori bounds for rough differential equations with a non-linear damping term
Authors: Bonnefoi, T
Chandra, A
Moinat, A
Weber, H
Item Type: Journal Article
Abstract: We consider a rough differential equation with a non-linear damping drift term: dY (t) = −|Y |m−1Y (t)dt + σ (Y (t))dX(t), where m>1, X is a (branched) rough path of arbitrary regularity α>0, and where σ is smooth and satisfies an m and α-dependent growth property. We show a strong a priori bound for Y, which includes the “coming down from infinity” property, i.e. the bound on Y(t) for a fixed t>0 holds uniformly over all choices of initial datum Y(0). The method of proof builds on recent work on a priori bounds for the ϕ4 SPDE in arbitrary subcritical dimension [7]. A key new ingredient is an extension of the algebraic framework which permits to derive an estimate on higher order conditions of a coherent controlled rough path in terms of the regularity condition at lowest level.
Issue Date: 5-May-2022
Date of Acceptance: 4-Feb-2022
URI: http://hdl.handle.net/10044/1/96114
DOI: 10.1016/j.jde.2022.02.006
ISSN: 0022-0396
Publisher: Elsevier BV
Start Page: 58
End Page: 93
Journal / Book Title: Journal of Differential Equations
Volume: 318
Copyright Statement: © 2022 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: 0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status: Published online
Online Publication Date: 2022-02-24
Appears in Collections:Pure Mathematics
Mathematics



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