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A Free Boundary Optimization Problem
SIAM Journal on Mathematical Analysis, 1978Given a convex set $Q \subset R^2 $ (bounded by a simple closed curve) and a constant $A > 0$, we determine the doubly-connected region $\Omega $ encircling (but not intersecting) Q, with area $| \Omega | \leqq A$, which has the least capacitance.
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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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Izvestiya: Mathematics, 2002
This paper deals with the regularity properties of solutions for the double nonlinear parabolic equation \[ u_t-D\left(u^{p_0}Du+| Du| ^{p_1}Du \right)=f(x,t). \tag{1} \] A Stefan-like problem for the one-dimensional analogue of equation (1) is also considered.
Soltanov, K. N., Novruzov, E. B.
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This paper deals with the regularity properties of solutions for the double nonlinear parabolic equation \[ u_t-D\left(u^{p_0}Du+| Du| ^{p_1}Du \right)=f(x,t). \tag{1} \] A Stefan-like problem for the one-dimensional analogue of equation (1) is also considered.
Soltanov, K. N., Novruzov, E. B.
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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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Nonlinear Analysis: Theory, Methods & Applications, 2008
We are concerned with the existence of positive solutions of the following discontinuous problem: \[ -\Delta u=f(u)H(u-\mu)\quad\text{in }\Omega, \qquad u=h\quad\text{on }\partial\Omega, \] where \(\Omega\) is the unit ball of \(\mathbb R^n\) \((n\geq 3)\) and \(H\)H is the Heaviside function.
Bensid, Sabri, Bouguima, S. M.
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We are concerned with the existence of positive solutions of the following discontinuous problem: \[ -\Delta u=f(u)H(u-\mu)\quad\text{in }\Omega, \qquad u=h\quad\text{on }\partial\Omega, \] where \(\Omega\) is the unit ball of \(\mathbb R^n\) \((n\geq 3)\) and \(H\)H is the Heaviside function.
Bensid, Sabri, Bouguima, S. M.
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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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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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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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On One Nonlocal Problem with Free Boundary
Ukrainian Mathematical Journal, 2001The author considers the equation \( \frac{\partial^2 u}{\partial x^2} + \frac{n-1}{x} \frac{\partial u}{\partial x} - g(u) \frac{\partial u} {\partial t}=0\), \(x,t\in{\mathbb R}_+^1\), \(n=1,2,3.\) The function \( g(u)\), \(u>0\) is positive, continuous, decreasing and has integrable singularity at the point \(u=0.\) By means of the functional \( f(u)
Mitropol'skij, Yu. A. +2 more
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Free Boundary Problems in Solidification of Alloys
SIAM Journal on Mathematical Analysis, 1980Multidimensional three-phase free boundary problems for semilinear diffusion equations are studied as models for the solidification (or melting) of alloys. The intermediate phase represents the “mushy zone” in which the freezing of the remaining liquid provides a heat generation effect.
Alexiades, Vasilios, Cannon, John R.
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