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