On the nature of space fluctuations of solutions of dissipative partial differential equations

Bartuccelli, Michele V. (2019) On the nature of space fluctuations of solutions of dissipative partial differential equations Applied Mathematics Letters, 96. pp. 14-19.

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Abstract

In this work we have analysed the nature of space fluctuations in dissipative Partial Differential Equations (PDEs). By taking a well known and much investigated dissipative PDE as our representative, namely the Swift–Hohenberg Equation, we estimated in an explicit manner the values of the crest factor of its solutions. We believe that the crest factor, namely the ratio between the sup-norm and the L² norm of solutions, is a suitable and proper measure of space fluctuations in solutions of dissipative PDEs. In particular it gives some information on the nature of “soft” and “hard” fluctuations regimes in the flows of dissipative PDEs.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Name Email ORCID Bartuccelli, Michele V. M.Bartuccelli@surrey.ac.uk
Date :	October 2019
DOI :	10.1016/j.aml.2019.04.011
Copyright Disclaimer :	© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords :	Dissipative partial differential equations; Best constants; Analysis of solutions; Crest factor
Depositing User :	Clive Harris
Date Deposited :	13 Jun 2019 07:47
Last Modified :	18 Apr 2020 02:08
URI:	http://epubs.surrey.ac.uk/id/eprint/851988

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