Hele-Shaw type problems with dynamical boundary conditions

Abstract In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation u t = Δ w + f where u ∈ H ( w ) and H is the Heaviside function, with boundary condition μ ( x , w ) ∂ t w + k ∇ w ⋅ ν = g , where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution.

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