A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade FluidReport as inadecuate




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Discrete Dynamics in Nature and Society - Volume 2016 2016, Article ID 3875324, 17 pages -

Research Article

University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang, Vietnam

The Faculty of Natural Basic Sciences, Vietnamese Naval Academy, 30 Tran Phu Street, Nha Trang, Vietnam

Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam

Received 18 September 2016; Accepted 13 November 2016

Academic Editor: Andrew Pickering

Copyright © 2016 Le Thi Phuong Ngoc et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the following initial-boundary value problem − + = , , ; , ; , where are given constants and and 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 for every In Part 2, we investigate asymptotic behavior of the solution as In Part 3, we prove the existence and uniqueness of a weak solution of problem − + = , , ; , associated with a -periodic condition- , where is given constant.





Author: Le Thi Phuong Ngoc, Truong Thi Nhan, and Nguyen Thanh Long

Source: https://www.hindawi.com/



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