scholarly journals Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

2008 ◽  
Vol 138 (6) ◽  
pp. 1345-1362 ◽  
Author(s):  
Eugen Varvaruca
Keyword(s):  
Free Boundary ◽  
Gravity Waves ◽  
Weak Solutions ◽  
Free Boundary Problems ◽  
Classical Problem ◽  
Finite Depth ◽  
Boundary Problems ◽  
Special Case ◽  
Bernoulli Free Boundary

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

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.

scholarly journals Topology optimization in Bernoulli free boundary problems

2012 ◽  
Vol 80 (1) ◽  
pp. 173-188 ◽  
Author(s):  
Jukka I. Toivanen ◽  
Raino A. E. Mäkinen ◽  
Jaroslav Haslinger
Keyword(s):  
Topology Optimization ◽  
Free Boundary ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Bernoulli Free Boundary

scholarly journals Fast Numerical Methods for Bernoulli Free Boundary Problems

2007 ◽  
Vol 29 (2) ◽  
pp. 622-634 ◽  
Author(s):  
Christopher M. Kuster ◽  
Pierre A. Gremaud ◽  
Rachid Touzani
Keyword(s):  
Numerical Methods ◽  
Free Boundary ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Bernoulli Free Boundary

Bernoulli free-boundary problems

2008 ◽  
Vol 196 (914) ◽  
pp. 0-0 ◽  
Author(s):  
E. Shargorodsky ◽  
J. F. Toland
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Bernoulli Free Boundary

Solvability of free boundary problems for steady groundwater flow

2015 ◽  
Vol 26 (6) ◽  
pp. 821-847 ◽  
Author(s):  
A. Yu. BELIAEV
Keyword(s):  
Variational Principle ◽  
Free Boundary ◽  
Weak Solutions ◽  
Input Data ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Phreatic Surface ◽  
Existence Of Weak Solutions ◽  
Lower Semi ◽  
Flow Domain

In this paper the free boundary problem for groundwater phreatic surface is represented in the form of a variational principle. It is proved that the flow domain Ω that solves the problem is a minimizer of some functional Λ(Ω). Weak solutions are introduced as minimizers of the lower semi-continuous regularization of Λ(⋅). Within this approach the existence of weak solutions is proved for a wide class of input data.

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
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