A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid
Joint Authors
Long, Nguyen Thanh
Nhan, Truong Thi
Ngoc, Le Thi Phuong
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-12-29
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We study the following initial-boundary value problem { u t − μ t + α t ( ∂ / ∂ t ) ∂ 2 u / ∂ x 2 + ( γ / x ) ( ∂ u / ∂ x ) + f u = f 1 x , t , 1 < x < R , t > 0 ; u ( 1 , t ) = g 1 ( t ) , u ( R , t ) = g R ( t ) ; u ( x , 0 ) = u ~ 0 ( x ) } , where γ > 0 , R > 1 are given constants and f , f 1 , g 1 , g R , u ~ 0 , α , and μ are given functions.
In Part 1, we use the Galerkin method and compactness method to prove the existence of a unique weak solution of the problem above on ( 0 , T ) , for every T > 0 .
In Part 2, we investigate asymptotic behavior of the solution as t → + ∞ .
In Part 3, we prove the existence and uniqueness of a weak solution of problem { u t − μ t + α t ( ∂ / ∂ t ) ∂ 2 u / ∂ x 2 + ( γ / x ) ( ∂ u / ∂ x ) + f u = f 1 x , t , 1 < x < R , t > 0 ; u ( 1 , t ) = g 1 ( t ) , u ( R , t ) = g R ( t ) } associated with a “ ( η , T ) -periodic condition” u ( x , 0 ) = η u ( x , T ) , where 0 < η ≤ 1 is given constant.
American Psychological Association (APA)
Ngoc, Le Thi Phuong& Nhan, Truong Thi& Long, Nguyen Thanh. 2016. A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid. Discrete Dynamics in Nature and Society،Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1103423
Modern Language Association (MLA)
Ngoc, Le Thi Phuong…[et al.]. A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid. Discrete Dynamics in Nature and Society No. 2016 (2016), pp.1-17.
https://search.emarefa.net/detail/BIM-1103423
American Medical Association (AMA)
Ngoc, Le Thi Phuong& Nhan, Truong Thi& Long, Nguyen Thanh. A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid. Discrete Dynamics in Nature and Society. 2016. Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1103423
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1103423