Asymptotic profiles for a class of perturbed Burgers equations in one space dimension

Asymptotic profiles for a class of perturbed Burgers equations in one space dimension

In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables \(\frac{\xi}{\sqrt\tau}\) and \(\log\tau\), we prove that the large time behavior of solutions...

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Main Authors: F. Dkhil, M. A. Hamza, B. Mannoubi
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2018-01-01
Series:Opuscula Mathematica
Subjects:
Burgers equation
self-similar variables
asymptotic behavior
self-similar solutions
Online Access:http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3804.pdf
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spelling doaj-e010bf478e9146b595f2212ad0aac9352020-11-24T20:59:22ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-013814180https://doi.org/10.7494/OpMath.2018.38.1.413804Asymptotic profiles for a class of perturbed Burgers equations in one space dimensionF. Dkhil0M. A. Hamza1B. Mannoubi2Université Tunis El Manar, Département de Mathématiques, Institut Supérieur d'Informatique, 2 rue Abou Raihan Bayrouni, 2080 Ariana, TunisiaDepartment of Basic Sciences, Deanship of Preparatory and Supporting Studies, Imam Abdulrahman Bin Faisal University, P.O. Box 1982 Dammam, Saudi ArabiaUniversité de Tunis El Manar, Faculté des Sciences de Tunis, UR13ES32 Analyse non linéaire et géometrie, 2092 Tunis, TunisiaIn this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables \(\frac{\xi}{\sqrt\tau}\) and \(\log\tau\), we prove that the large time behavior of solutions is given by the self-similar solutions of the associated Burgers equation.http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3804.pdfBurgers equationself-similar variablesasymptotic behaviorself-similar solutions
collection DOAJ
language English
format Article
sources DOAJ
author F. Dkhil
M. A. Hamza
B. Mannoubi
spellingShingle F. Dkhil
M. A. Hamza
B. Mannoubi
Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
Opuscula Mathematica
Burgers equation
self-similar variables
asymptotic behavior
self-similar solutions
author_facet F. Dkhil
M. A. Hamza
B. Mannoubi
author_sort F. Dkhil
title Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
title_short Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
title_full Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
title_fullStr Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
title_full_unstemmed Asymptotic profiles for a class of perturbed Burgers equations in one space dimension
title_sort asymptotic profiles for a class of perturbed burgers equations in one space dimension
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2018-01-01
description In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables \(\frac{\xi}{\sqrt\tau}\) and \(\log\tau\), we prove that the large time behavior of solutions is given by the self-similar solutions of the associated Burgers equation.
topic Burgers equation
self-similar variables
asymptotic behavior
self-similar solutions
url http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3804.pdf
work_keys_str_mv AT fdkhil asymptoticprofilesforaclassofperturbedburgersequationsinonespacedimension
AT mahamza asymptoticprofilesforaclassofperturbedburgersequationsinonespacedimension
AT bmannoubi asymptoticprofilesforaclassofperturbedburgersequationsinonespacedimension
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