Existence of Weak Solutions for a Nonlinear Elliptic System. (26th August 2009) - Fang, Ming; Gilbert, Robert P.
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− Δ θ = k ( θ ) | ∇ p | r + q ( x ) inΩ ;− div ( k ( θ ) | ∇ p | r − 2 + β ( x ) | ∇ p | r 0 − 2 ) ∇ p = 0 inΩ ;θ = θ 0, andp = p 0 on∂ Ω .