Diffuse-Interface Approximations of Osmosis Free Boundary Problems

Diffuse-Interface Approximations of Osmosis Free Boundary Problems

Free boundary problems based on mass conservation and surface tension with application in osmotic swelling are the topic of this contribution. Phase-field approximations of such models are introduced, in order to numerically investigate properties of the solutions. Formal justification of the proposed approximations is provided by matched asymptotic expansions supported by numerical tests repro...

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...

Exterior Boundary Value Problems as Limits of Interface Problems

It is proved that the solution to exterior Neumann boundary value problem can be obtained as the limit of the solutions of some problems in the whole space. 1 Consider the following problem: (V' + k*)u =f in f2, ul,=O, where f2 = R3\D. D is bounded domain with a smooth boundary r, fE C,(Q), k > 0. In [l] we proved the following: THEOREM 1. Consider the problem V=N in D N = const. > 0. =0 in Q, ...

Galerkin Approximations of Abstract Parabolic Boundary Value Problems

Galerkin approximations of an abstract parabolic boundary value problem with "rough" boundary data are considered. The optimal rates of convergence in Lp[0T; L2(ti)] norms for L [07"; L2(T)] boundary terms are derived.