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Showing 1 to 19 of 19 for “"free boundary problem"”.
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Regularity of Neumann solutions to an elliptic free boundary problem
… properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary …
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A free boundary problem inspired by a conjecture of De Giorgi
We study global monotone solutions of the free boundary problem that arises from minimizing the energy functional I(u) = f lVul2 + V(U), where V(u) is the characteristic function of the interval (-1, 1). This functional is a close relative of the scalar Ginzburg-Landau functional J(u) = f lVul2 + …
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Existence and regularity of monotone solutions to a free boundary problem
… first example of a singular energy minimizing free boundary. This singular solution occurs in dimension 7 and higher, and in fact it is conjectured that there are no singular minimizers in dimension lower than 7. Our example is the analogue of the 8-dimensional Simons cone in the theory of …
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Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2
This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary …
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Adjoint Error Estimation for Elastohydrodynamic Lubrication
… to complex elastohydrodynamic lubrication (EHL) problems. A functional is introduced, namely the friction, and justification is provided as to why this quantity, and hence its accuracy, is important. An iterative approach has been taken to develop understanding of the mechanisms at work. A series …
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Modeling hotspot dynamics in microwave heating
… analysis is used to reduce the system to a free boundary problem. This approximation accurately predicts the steady-state solutions for the temperature and electric fields in closed form. These solutions are valid for arbitrary values of the electric conductivity, and thus extend the …
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Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients
… this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity …
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The pricing of multiple exercisable American-style real options
… at the end. This dissertation also addresses the problem of tracking early exercise boundaries in pricing American-style real options. It is shown that both models provide effective numerical solutions to the free boundary problem"--Abstract, page iii.</p>
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A Numerical Scheme for Mullins-Sekerka Flow in Three Space Dimensions
<p>The Mullins-Sekerka problem, also called two-sided Hele-Shaw flow, arises in modeling a binary material with two stable concentration phases. A coarsening process occurs, and large particles grow while smaller particles eventually dissolve. Single particles become spherical. This process is …
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Oscillations of a Fluid in a Channel
… with the motion of the fluid, so we deal with a free boundary problem. We consider small perturbations of a uniform flow with a flat free surface. We include the effect of the surface tension; the external forces are gravity, and the wind force which acts on the free boundary. The motion of the …
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Optimal Stopping Problems with A Random Time Horizon
… the study of American contingent claim pricing problem in mathematical finance. We give a self-contained overview of the theory, including the complete proofs of existence and uniqueness theorems for the optimal stopping time in finite-time formulation. These theorems are developed with the goal …
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The stabilization and extinction of a microjet diffusion flame
… is confined to a surface and the mathematical problem reduces to a free boundary problem with jump relations across the flame sheet. Constant density approximation decouples the hydrodynamic equations from the full system of governing equations. The flow field is described by an exact solution …
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Principio di linearizzazione per problemi a frontiera libera della fluidodinamica
Studiamo il moto di onde superficiali periodiche nello spazio. Uno strato infinito di fluido incompressibile viscoso e Newtoniano è limitato inferiormente da un piano e superiormente da una superficie libera. Sul fluido agiscono forze idrodinamiche, ed il moto risultante è supposto periodico …
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Modeling and control of cadmium zinc telluride grown via an electro-dynamic gradient freeze furnace.
… complement formulation is employed to solve the free-boundary problem associated with melt crystal growth systems. With this form, the difficult interface location part of the problem is mapped away from the equations governing transport. We assess the behavior of this method using …
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New results in stochastic moving boundary problems
Moving boundary problems arise in many areas of science and engineering and they are of great importance in the areas of partial differential equations (PDEs) since they characterize phase change phenomena where a system has two phases such as solid and liquid. However, unlike other PDEs in a …
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Spreading of viscous fluids and granular materials on slopes
… of the flowing structure. Numerous different problems are investigated through mathematical models, which are developed analytically and confirmed by laboratory experiments. The initial advance of long lava flows is studied by considering the flow of viscous fluid released on sloping channels. …
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Brownian particles interacting with a Newtonian Barrier: Skorohod maps and their use in solving a PDE with free boundary, strong approximation, and hydrodynamic limits.
… and uniqueness of the resulting PDE with free boundary condition. In 2001, Frank Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. …
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Brownian motion and multidimensional decision making
… theory and path integrals. Part II, "The problem of alternatives", considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected …
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Level set methods for higher order evolution laws
… an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The …