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On the crest factor for dissipative partial differential equations

Bartuccelli, Michele V. (2019) On the crest factor for dissipative partial differential equations Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2229).

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In this work, we have introduced and then computed the so-called crest factor associated with solutions of dissipative partial differential equations (PDEs). By taking two paradigmatic dissipative PDEs, we estimated in an explicit and accurate manner the values of the crest factor of their solutions. We then analysed and compared the estimates as a function of the positive parameter which appears in the PDEs in space dimensions one and two. These estimates shed some light on the dynamics of the fluctuations of the solutions of the two model PDEs, and therefore provide a criterion for discerning between small and large potential excursions in space for the solution of any dissipative PDE. Being able to detect between small and large intermittent fluctuations is one of the hallmarks of turbulence. We believe that the crest factor is an appropriate tool for extracting space fluctuation features in solutions of dissipative PDEs.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bartuccelli, Michele
Date : 4 September 2019
DOI : 10.1098/rspa.2019.0322
Copyright Disclaimer : © 2019 The Author(s). Published by the Royal Society. All rights reserved.
Uncontrolled Keywords : Dissipative Partial Differential Equations; Interpolation Inequalities; Best Constants; Analysis of Solutions; Crest Factor
Depositing User : Clive Harris
Date Deposited : 20 Sep 2019 12:46
Last Modified : 20 Sep 2019 12:46

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