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...
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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 |
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1721193490802540544 |