Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4604394 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2012 | 23 Pages |
Abstract
The existence and uniqueness of weak solutions are studied to the initial Dirichlet problem of the equationut=div(|∇u|p(x)−2∇u)+f(x,t,u),ut=div(|∇u|p(x)−2∇u)+f(x,t,u), with infp(x)>2. The problems describe the motion of generalized Newtonian fluids which were studied by some other authors in which the exponent p was required to satisfy a logarithmic Hölder continuity condition. The authors in this paper use a difference scheme to transform the parabolic problem to a sequence of elliptic problems and then obtain the existence of solutions with less constraint to p(x)p(x). The uniqueness is also proved.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Songzhe Lian, Wenjie Gao, Hongjun Yuan, Chunling Cao,