Some Results About a Boundary Value Problem on Mixed Convection

The purpose of this paper is to study the autonomous third order non linear differential equation f’’’ + ff’’ + g(f’) = 0 on [0, +∞[ with g(x) = βx(x − 1) and β > 1, subject to the boundary conditions f(0) = a ∈ R, f’(0) = b < 0 and f’(t) → λ ∈ {0, 1} as t → +∞. This problem arises whe...

Full description

Bibliographic Details
Main Authors: M. Boulekbache, M. Aiboudi, K. Boudjema Djeffal
Format: Article
Language:English
Published: Etamaths Publishing 2020-05-01
Series:International Journal of Analysis and Applications
Online Access:http://etamaths.com/index.php/ijaa/article/view/2037
id doaj-7461e478479343518ba59d4160b77182
record_format Article
spelling doaj-7461e478479343518ba59d4160b771822021-08-26T13:44:40ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392020-05-01183356365448Some Results About a Boundary Value Problem on Mixed ConvectionM. Boulekbache0M. Aiboudi1K. Boudjema Djeffal2Université oran1 Ahmed ben balla Université hassiba ben bouali CHLEFUniversité oran1 Ahmed Ben ballaUniversité de Haute-Alsace, LMIA EA 1108, F-68100 Mulhouse, FranceThe purpose of this paper is to study the autonomous third order non linear differential equation f’’’ + ff’’ + g(f’) = 0 on [0, +∞[ with g(x) = βx(x − 1) and β > 1, subject to the boundary conditions f(0) = a ∈ R, f’(0) = b < 0 and f’(t) → λ ∈ {0, 1} as t → +∞. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as mixed convection in porous medium or flow adjacent to a stretching wall. Our goal, here is to investigate by a direct approach this boundary value problem as completely as possible, say study existence or non-existence and uniqueness solutions and the sign of this solutions according to the value of the real parameter β.http://etamaths.com/index.php/ijaa/article/view/2037
collection DOAJ
language English
format Article
sources DOAJ
author M. Boulekbache
M. Aiboudi
K. Boudjema Djeffal
spellingShingle M. Boulekbache
M. Aiboudi
K. Boudjema Djeffal
Some Results About a Boundary Value Problem on Mixed Convection
International Journal of Analysis and Applications
author_facet M. Boulekbache
M. Aiboudi
K. Boudjema Djeffal
author_sort M. Boulekbache
title Some Results About a Boundary Value Problem on Mixed Convection
title_short Some Results About a Boundary Value Problem on Mixed Convection
title_full Some Results About a Boundary Value Problem on Mixed Convection
title_fullStr Some Results About a Boundary Value Problem on Mixed Convection
title_full_unstemmed Some Results About a Boundary Value Problem on Mixed Convection
title_sort some results about a boundary value problem on mixed convection
publisher Etamaths Publishing
series International Journal of Analysis and Applications
issn 2291-8639
publishDate 2020-05-01
description The purpose of this paper is to study the autonomous third order non linear differential equation f’’’ + ff’’ + g(f’) = 0 on [0, +∞[ with g(x) = βx(x − 1) and β > 1, subject to the boundary conditions f(0) = a ∈ R, f’(0) = b < 0 and f’(t) → λ ∈ {0, 1} as t → +∞. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as mixed convection in porous medium or flow adjacent to a stretching wall. Our goal, here is to investigate by a direct approach this boundary value problem as completely as possible, say study existence or non-existence and uniqueness solutions and the sign of this solutions according to the value of the real parameter β.
url http://etamaths.com/index.php/ijaa/article/view/2037
work_keys_str_mv AT mboulekbache someresultsaboutaboundaryvalueproblemonmixedconvection
AT maiboudi someresultsaboutaboundaryvalueproblemonmixedconvection
AT kboudjemadjeffal someresultsaboutaboundaryvalueproblemonmixedconvection
_version_ 1721193490802540544