Boundary Value Problems
Volume 2009 (2009), Article ID 708389, 15 pages
doi:10.1155/2009/708389
Research Article

Existence of Weak Solutions for a Nonlinear Elliptic System

Ming Fang1 and Robert P. Gilbert2

1Department of Mathematics, Norfolk State University, Norfolk, VA 23504, USA
2Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

Received 3 April 2009; Accepted 31 July 2009

Academic Editor: Kanishka Perera

Copyright © 2009 Ming Fang and Robert P. Gilbert . 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 investigate the existence of weak solutions to the following Dirichlet boundary value problem, which occurs when modeling an injection molding process with a partial slip condition on the boundary. We have −Δθ=k(θ)|∇p|r+q(x) in Ω; −div{(k(θ)|∇p|r−2+β(x)|∇p|r0−2)∇p}=0 in Ω; θ=θ0, and p=p0 on ∂Ω.