Elsevier

Applied Mathematics Letters

Volume 96, October 2019, Pages 14-19
Applied Mathematics Letters

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

https://doi.org/10.1016/j.aml.2019.04.011Get rights and content
Under an Elsevier user license
open archive

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.

Keywords

Dissipative partial differential equations
Best constants
Analysis of solutions
Crest factor

Cited by (0)