A vortex free boundary problem: Existence and uniqueness results for the physical solution

1997 ◽  
Vol 173 (1) ◽  
pp. 279-298
Author(s):  
Alessandro Torelli
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness ◽  
Physical Solution ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

A free surface problem arising in the drainage of a uniformly irrigated field: Existence and uniqueness results

1984 ◽  
Vol 36 (3) ◽  
pp. 389-403 ◽  
Author(s):  
John Van Der Hoek ◽  
C. J. Barnes ◽  
J. H. Knight
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Value Problem ◽  
Variational Inequalities ◽  
Existence And Uniqueness ◽  
Free Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Tile Drains ◽  
Porous Soil

AbstractA field comprising uniformly porous soil overlying an impervious subsoil is drained through equally spaced tile drains placed on the boundary between the two layers of soil. When this field is subject to uniform irrigation, a free boundary forms in the porous region above the zone of saturation. We study the free boundary value problem which thus arises using the theory of variational inequalities. Existence and uniqueness results are established.

scholarly journals A non-local free boundary problem arising in a theory of financial bubbles

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130404 ◽  
Author(s):  
Henri Berestycki ◽  
Regis Monneau ◽  
José A. Scheinkman
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness ◽  
Obstacle Problem ◽  
Speculative Bubbles ◽  
Financial Bubbles ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
The Cost

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c , the cost of transacting the asset, goes to zero.

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