Self similar solutions of generalized Burgers equation

In this paper, we study the initial-value problem $$displaylines{ (|u'|^{p-2}u')'+eta r u'+alpha u-gamma |u|^{q-1}u|u'|^{p-2}u'=0, quad r greater than 0, cr u(0)=A,quad u'(0)=0, }$$ where $A$ greater than 0, $p$ greater than 2, $q greater than 1, $alpha greater tha...

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Main Authors: Abdelilah Gmira, Ahmed Hamydy, Salek Ouailal
Format: Article
Language:English
Published: Texas State University 2005-07-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2005/80/abstr.html
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author Abdelilah Gmira
Ahmed Hamydy
Salek Ouailal
author_facet Abdelilah Gmira
Ahmed Hamydy
Salek Ouailal
author_sort Abdelilah Gmira
collection DOAJ
description In this paper, we study the initial-value problem $$displaylines{ (|u'|^{p-2}u')'+eta r u'+alpha u-gamma |u|^{q-1}u|u'|^{p-2}u'=0, quad r greater than 0, cr u(0)=A,quad u'(0)=0, }$$ where $A$ greater than 0, $p$ greater than 2, $q greater than 1, $alpha greater than 0, $eta greater than 0 and $ gamma in{mathbb{R}}$. Existence and complete classification of solutions are established. Asymptotic behavior for nonnegative solutions is also presented.
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spelling doaj.art-bd402403d3b6445088fd524eb7d518fc2022-12-21T19:29:38ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-07-01200580122Self similar solutions of generalized Burgers equationAbdelilah GmiraAhmed HamydySalek OuailalIn this paper, we study the initial-value problem $$displaylines{ (|u'|^{p-2}u')'+eta r u'+alpha u-gamma |u|^{q-1}u|u'|^{p-2}u'=0, quad r greater than 0, cr u(0)=A,quad u'(0)=0, }$$ where $A$ greater than 0, $p$ greater than 2, $q greater than 1, $alpha greater than 0, $eta greater than 0 and $ gamma in{mathbb{R}}$. Existence and complete classification of solutions are established. Asymptotic behavior for nonnegative solutions is also presented.http://ejde.math.txstate.edu/Volumes/2005/80/abstr.htmlBurgers equationself similarclassificationasymptotic behavior.
spellingShingle Abdelilah Gmira
Ahmed Hamydy
Salek Ouailal
Self similar solutions of generalized Burgers equation
Electronic Journal of Differential Equations
Burgers equation
self similar
classification
asymptotic behavior.
title Self similar solutions of generalized Burgers equation
title_full Self similar solutions of generalized Burgers equation
title_fullStr Self similar solutions of generalized Burgers equation
title_full_unstemmed Self similar solutions of generalized Burgers equation
title_short Self similar solutions of generalized Burgers equation
title_sort self similar solutions of generalized burgers equation
topic Burgers equation
self similar
classification
asymptotic behavior.
url http://ejde.math.txstate.edu/Volumes/2005/80/abstr.html
work_keys_str_mv AT abdelilahgmira selfsimilarsolutionsofgeneralizedburgersequation
AT ahmedhamydy selfsimilarsolutionsofgeneralizedburgersequation
AT salekouailal selfsimilarsolutionsofgeneralizedburgersequation