Hele-Shaw type problems with dynamical boundary conditions

[摘要] In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation u(t) = Delta w + f where u is an element of H(w) and H is the Heaviside function, with boundary condition mu(x, w)partial derivative(1) w + k del w . v = g, where v denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] Hele-Shaw problem;dynamical boundary condition;Neumann boundary condition;evolution problem;nonlinear semigroup theory