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Plane free-boundary equilibria
Plasma Physics and Controlled Fusion, 1991The free-boundary MHD equilibrium is considered for plane symmetry and a constant current profile. The field produced by external currents is prescribed and the plasma current is determined such that the plasma extends up to the separatrix.
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Free-boundary high-beta tokamaks. III. Free-boundary stability
The Physics of Fluids, 1982Using the techniques of Hilbert transforms and conformal mapping, the stability problem of a toroidal free-boundary high-β tokamak equilibrium with a skin current is reduced to a one-dimensional problem for which a new variational principle is derived.
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2013
As we know, a problem of pricing an American-style derivative can be formulated as a linear complementarity problem, and for most cases, it can also be written as a free-boundary problem. In Chap. 8, we have discussed how to solve a linear complementarity problem. Here, we study how to solve a free-boundary problem numerically. Many derivative security
You-lan Zhu +3 more
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As we know, a problem of pricing an American-style derivative can be formulated as a linear complementarity problem, and for most cases, it can also be written as a free-boundary problem. In Chap. 8, we have discussed how to solve a linear complementarity problem. Here, we study how to solve a free-boundary problem numerically. Many derivative security
You-lan Zhu +3 more
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1983
One example of a flow with a free boundary is that of a jet of fluid travelling through a region of constant pressure. There are two typical situations which are shown in Figure. The first is a jet impinging on a fixed wall and the second is a jet emerging from a hole in the wall of a large reservoir.
Hilary Ockendon, Alan B. Tayler
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One example of a flow with a free boundary is that of a jet of fluid travelling through a region of constant pressure. There are two typical situations which are shown in Figure. The first is a jet impinging on a fixed wall and the second is a jet emerging from a hole in the wall of a large reservoir.
Hilary Ockendon, Alan B. Tayler
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Mathematical Methods in the Applied Sciences, 1996
Summary: This paper considers a discontinuous semilinear elliptic problem: \[ - \Delta u= g(u)H(u-\mu) \quad \text{in } \Omega, \qquad u=h \text{ on } \partial \Omega, \] where \(H\) is the Heaviside function, \(\mu\) a real parameter and \(\Omega\) the unit ball in \(\mathbb{R}^2\). We deal with the existence of solutions under suitable conditions on \
Boucherif, Abdelkader +1 more
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Summary: This paper considers a discontinuous semilinear elliptic problem: \[ - \Delta u= g(u)H(u-\mu) \quad \text{in } \Omega, \qquad u=h \text{ on } \partial \Omega, \] where \(H\) is the Heaviside function, \(\mu\) a real parameter and \(\Omega\) the unit ball in \(\mathbb{R}^2\). We deal with the existence of solutions under suitable conditions on \
Boucherif, Abdelkader +1 more
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2003
Abstract This chapter is the most unconventional in the book. Whereas hyperbolic, elliptic and parabolic problems have been studied over many decades, and many texts are devoted to each, the subject of free boundary problems has attracted few specialised publications despite its importance in modern applied mathematics.
John Ockendon +3 more
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Abstract This chapter is the most unconventional in the book. Whereas hyperbolic, elliptic and parabolic problems have been studied over many decades, and many texts are devoted to each, the subject of free boundary problems has attracted few specialised publications despite its importance in modern applied mathematics.
John Ockendon +3 more
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2017
Obstacle and contact problems leading to variational inequalities as well as models for porous media are studied. A main theme is phase transitions appearing in the context of solidification processes. Finally, also free boundary problems in fluid dynamics are considered.
Christof Eck +2 more
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Obstacle and contact problems leading to variational inequalities as well as models for porous media are studied. A main theme is phase transitions appearing in the context of solidification processes. Finally, also free boundary problems in fluid dynamics are considered.
Christof Eck +2 more
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One-Layer Free Boundary Problems with Two Free Boundaries
2005We study the uniqueness and successive approximation of solutions of a class of two-dimensional steady-state fluid problems involving infinite periodic flows between two periodic free boundaries, each characterized by a flow-speed condition related to Bernoulli’s law.
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1993
Abstract The equations derived thus far combine to form an important free-boundary problem for the temperature. The differential equation to be satisfied in bulk is balance of energy supplemented by the constitutive equations (cf. (14.27)): [eq]The evolving interface forms a free boundary, and the corresponding free-boundary conditions ...
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Abstract The equations derived thus far combine to form an important free-boundary problem for the temperature. The differential equation to be satisfied in bulk is balance of energy supplemented by the constitutive equations (cf. (14.27)): [eq]The evolving interface forms a free boundary, and the corresponding free-boundary conditions ...
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Boundary regularity for free boundary problems
Communications on Pure and Applied Mathematics, 1999The purpose of this paper is to study up-to-the-boundary regularity of solutions of elliptic free boundary problems with two phases. The solution of a typical problem can be described as a function \(u\) that is harmonic in \(\{u\neq 0\}\) and satisfies the gradient jump condition: \(| \nabla u^+|^2 -|\nabla u^-|^2=1\) on the free boundary \(\{u= 0\}\).
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