General free boundary evolution problems in several space dimensions
نویسندگان
چکیده
منابع مشابه
Numerical Approximation of a Parabolic Problem with a Nonlinear Boundary Condition in Several Space Dimensions
In this paper we study the asymptotic behaviour of a semidiscrete numerical approximation for the heat equation, ut = ∆u, in a bounded smooth domain, with a nonlinear flux boundary condition at the boundary, ∂u ∂η = up. We focus in the behaviour of blowing up solutions. First we prove that every numerical solution blows up in finite time if and only if p > 1 and that the numerical blow-up time ...
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Every solution of a linear elliptic equation on a bounded domain may be considered as an equilibrium of a free boundary problem. The free boundary problem consists of the corresponding parabolic equation on a variable unknown domain with free boundary conditions prescribing both Dirichlet and Neumann data. We establish a rigorous stability analysis of such equilibria, including the construction...
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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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1983
ISSN: 0022-247X
DOI: 10.1016/0022-247x(83)90140-3