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 11 of 11 for “"Elliptic PDEs"”.
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Discretization and solution of elliptic PDEs--a transform domain approach
Includes bibliographies.
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Intrinsic Lipschitz graphs in Heisenberg groups and non linear sub-elliptic PDEs
In this thesis we study intrinsic Lipschitz functions. In particular we provide a regular approximation result and a Poincarè type inequality for this class of functions. Moreover we study the obstacle problem in the Heisenberg group and we prove a geometric Poincarè inequality for a class of …
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Galerkin Projections Between Finite Element Spaces
… approximating spaces when solving elliptic PDEs with Galerkin finite element methods. For nonlinear PDEs, solving the nonlinear problem with Newton's method requires an initial guess of the solution on a refined space, which can be found by interpolating the solution from a previous …
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Full Stability In Optimization
… optimal control problems governed by semilinear elliptic PDEs are also studied.</p>
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some useful …
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Graphs, Principal Minors, and Eigenvalue Problems
… embedding to trace theorems from the theory of elliptic PDEs, and we provide a rigorous theoretical analysis of the popular Kamada-Kawai objective, proving hardness of approximation and structural results regarding optimal layouts, and providing a polynomial time randomized approximation scheme …
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Boundary Value Problems for the Laplace Equation on Convex Domains with Analytic Boundary
… global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth …
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Approximation of random/stochastic partial differential equations
… of partial differential equations (PDEs) with randomness or stochasticity. We focus on three rather different problems: a study of random fields on spherical shells, and its applications to PDE problems; quasi-Monte Carlo (QMC) methods for a class of PDEs with random coefficients; …
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Toward computational oncology: nonlinear simulation of centimeter-scale tumour growth in complex, heterogeneous tissues
… can accurately and efficiently solve nonlinear elliptic PDEs on large, complex domains, even withgeometry-dependent jump boundary conditions. After testing the new technique, we simulate the growth of glioblastoma (an aggressive brain tumor) in a large, 1 cm square of brain tissue that includes …
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Nonlinear Methods in the Study of Singular Partial Differential Equations
… to investigate a large class of nonlinear elliptic PDEs underlying models from physical and biological sciences. These methods advance the knowledge of qualitative properties of the solutions to equations of the form &Delta u= &fnof(x,u) where &Omega is a smooth domain in R^N (bounded or …
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Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations
We study a parameter identification problem for the steady state diffusion equations. In this thesis, we transform this identification problem into a minimization problem by considering an appropriate cost functional and propose a finite element method for the identification of the parameter for …