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...
Main Authors: | , , |
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Format: | Article |
Language: | English |
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Texas State University
2005-07-01
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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. |
first_indexed | 2024-12-20T18:48:42Z |
format | Article |
id | doaj.art-bd402403d3b6445088fd524eb7d518fc |
institution | Directory Open Access Journal |
issn | 1072-6691 |
language | English |
last_indexed | 2024-12-20T18:48:42Z |
publishDate | 2005-07-01 |
publisher | Texas State University |
record_format | Article |
series | Electronic Journal of Differential Equations |
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 |