Nonlinear enhanced dissipation in viscous Burgers type equations II

Tej Eddine Ghoul; Nader Masmoudi; Eliot Pacherie

doi:10.1080/03605302.2023.2277453

Nonlinear enhanced dissipation in viscous Burgers type equations II

Tej Eddine Ghoul, Nader Masmoudi, Eliot Pacherie

Research output: Contribution to journal › Article › peer-review

Abstract

In this follow up but self contained paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of infinite mass initial datas. We show that an enhanced dissipation effect occurs generically, that is the decay rate in time is better than if we considered instead the heat equations for the same inital value. We also show the existence of a kind of global attractor per class.

Original language	English (US)
Pages (from-to)	1286-1322
Number of pages	37
Journal	Communications in Partial Differential Equations
Volume	48
Issue number	10-12
DOIs	https://doi.org/10.1080/03605302.2023.2277453
State	Published - 2023

Keywords

asymptotic profiles
nonlinear analysis
self similar transformations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2023.2277453

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keywords = "asymptotic profiles, nonlinear analysis, self similar transformations",

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AU - Masmoudi, Nader

AU - Pacherie, Eliot

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AB - In this follow up but self contained paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of infinite mass initial datas. We show that an enhanced dissipation effect occurs generically, that is the decay rate in time is better than if we considered instead the heat equations for the same inital value. We also show the existence of a kind of global attractor per class.

KW - asymptotic profiles

KW - nonlinear analysis

KW - self similar transformations

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JF - Communications in Partial Differential Equations

IS - 10-12

ER -

Nonlinear enhanced dissipation in viscous Burgers type equations II

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Keywords

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