Hele-Shaw type problems with dynamical boundary conditions |
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Authors: | Noureddine Igbida |
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Affiliation: | LAMFA, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80038 Amiens, France |
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Abstract: | In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+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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Keywords: | Hele-Shaw problem Dynamical boundary condition Neumann boundary condition Evolution problem Nonlinear semigroup theory |
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