A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second‐Grade Fluid

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

Discrete Dynamics in Nature and Society, 2016, vol. 2016, issue 1

Abstract: We study the following initial‐boundary value problem {ut − (μ(t) + α(t)(∂/∂t))(∂2u/∂x2 + (γ/x)(∂u/∂x)) + f(u) = f1(x, t), 1 0; u(1, t) = g1(t), u(R, t) = gR(t); u(x,0)=u~0(x)}, where γ > 0, R > 1 are given constants and f, f1, g1, gR, 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 {ut − (μ(t) + α(t)(∂/∂t))(∂2u/∂x2 + (γ/x)(∂u/∂x)) + f(u) = f1(x, t), 1 0; u(1, t) = g1(t), u(R, t) = gR(t)} associated with a “(η, T)‐periodic condition” u(x, 0) = ηu(x, T), where 0

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2016/3875324

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:3875324

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().