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A free boundary problem of wave equation (Free Boundary Problems)

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Free Boundary Problem

SIAM Journal on Mathematical Analysis, 1974
Let $\mathcal{D}$ be a doubly connected region in the complex plane limited by the infinite point and a convex set $\Gamma $. If $\lambda > 0$, then we study the existence, uniqueness and geometry of annuli $\omega \subset \mathcal{D}$ having $\Gamma $ as one boundary component and another boundary component $\gamma $, such that there exists a harmonic
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Free-Boundary Problems

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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On a Free Boundary Problem

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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Free Boundary Problems

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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Free boundary problems

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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