scholarly journals Free boundary problems with radiation boundary conditions

1979 ◽  
Vol 37 (1) ◽  
pp. 1-10 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary

scholarly journals On the existence of non-flat profiles for a Bernoulli free boundary problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Giovanni Gravina ◽  
Giovanni Leoni
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Dirichlet Boundary ◽  
Free Boundary Problems ◽  
Energy Functional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Problems ◽  
Global Minimizers ◽  
Flat Profile

AbstractIn this paper, we consider a large class of Bernoulli-type free boundary problems with mixed periodic-Dirichlet boundary conditions. We show that solutions with non-flat profile can be found variationally as global minimizers of the classical Alt–Caffarelli energy functional.

Properties of some ordinary differential equations related to free boundary problems

1986 ◽  
Vol 104 (3-4) ◽  
pp. 217-234 ◽  
Author(s):  
Gunduz Caginalp ◽  
Stuart Hastings
Keyword(s):  
Phase Transition ◽  
Free Boundary ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Phase Field ◽  
Free Boundary Problems ◽  
Second Order ◽  
Boundary Problems ◽  
Field Approach

SynopsisSome second order ordinary differential equations of the form ξ2ϕ″ + ξ2(N − 1)″′/r + ½(ϕ − ϕ3) + ½k = 0 are studied. Properties such as existence and monotonicity of solutions are considered for N ≧ 1, ξ > 0 and two sets of boundary conditions. For N = 1, some explicit results are obtained for small ξ. These ODE's arise from a phase field approach to free boundary problems involving a phase transition.

scholarly journals On optimal regularity of free boundary problems and a conjecture of De Giorgi

2005 ◽  
Vol 58 (8) ◽  
pp. 1051-1076 ◽  
Author(s):  
Herbert Koch ◽  
Giovanni Leoni ◽  
Massimiliano Morini
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Optimal Regularity ◽  
Boundary Problems

scholarly journals On the Two-phase Fractional Stefan Problem

2020 ◽  
Vol 20 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Félix del Teso ◽  
Jørgen Endal ◽  
Juan Luis Vázquez
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Free Boundary Problems ◽  
Classical Problem ◽  
Nonlocal Diffusion ◽  
Two Phase ◽  
Boundary Problems ◽  
Numerical Studies ◽  
The One ◽  
Evolution Type

AbstractThe classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest to us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem, which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem, which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.

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