Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 35 for “"boundary problem"”.
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On a Moving Boundary Problem of Transitional Ballistics
<p>A major problem which arises in computer simulation of the firing of a gun weapon is the development of numerical schemes which effectively account for the physics of projectile motion. The chief difficulty is that away from the projectile the calculation is ordinarily accomplished on a fixed …
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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
… 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 minimal …
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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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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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Mathematical Modeling and Scanning Electron Microscopic Study of Biofilm on Adsorptive Media (Orthogonal Collocation Method)
… substrate diffuses in a growing biofilm (moving boundary problem); the reaction term is nonlinear; and substrate diffuses in a layered-media. An advanced numerical technique, the Global Orthogonal Collocation Method, was employed to solve the model.
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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 previous …
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Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients
… 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 solutions …
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Nonlinear simulation of tumor growth and chemotherapy
We implement numerically a model for free boundary necrotic and non-necrotic tumor growth and chemotherapy, where the tumor-healthy tissue interface is a moving deformable boundary. In the process, we improve upon existing techniques and develop new finite difference and ghost fluid / level set …
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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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Supercritical Semi-Linear Elliptic Problems Using Variational Principles
… The work covers two supercritical elliptic problems with different boundary conditions. First, it establishes the existence of a nontrivial solution for a Neumann problem in the unit ball, where the nonlinearity f(u) has a continuous primitive. Then, the dissertation explores a Dirichlet …
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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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Multiscale Mathematical Modelling of Cancer Invasion
… by applying a level-set method to a moving boundary problem. Later, a multi-scale mathematical model of cancer invasion was developed by coupling the urokinase plasminogen activation (uPA) system with a two-scale computational modelling technique. This approach allows us to investigate …
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Morse inequalities, a probabilistic approach
… estimation of a solution to a parabolic initial-boundary problem on a ball in the Euclidean space. We achieve that by constructing a supersolution. For the case the point is close to the critical set, we use an integration by parts in the Malliavin calculus and split the analysis for paths …
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A numerical method for electro-kinetic flow with deformable interfaces
… and fluid dynamics in the Debye layer into a boundary integral numerical solution of the full moving boundary problem. We present solutions for the quasi-steady state problem with [psi] = O(1) and solutions for the time dependent problem with [psi] [netsted less less] 1, where [psi] is the …
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Oscillations of a Fluid in a Channel
… 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 fluid …
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Aiding automated testing generation process by visualizing dynamic symbolic execution
… tools often experience three main categories of problems: the object creation problem, external method call problem, and boundary problem. When these problems arise, the testing tools present little information about the problem causes, leaving the users in the dark. Furthermore, there is little …
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