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 38 for “"existence of solutions"”.
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Existence of Solutions Via a New Variational Principle for Nonlocal Semilinear Elliptic Equations
The aim of this thesis is to prove the existence of a weak solution for semilinear fractional elliptic equations given by \begin{eqnarray*}\left\{ \begin{array}{ll} (-\Delta)^s u=|u|^{p-2} u+ f(x),& \quad x\in \Omega,\\ u=0, & \quad x \in \R^n \backslash \Omega, %0, & \quad x \in \partial \Oemga, …
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Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions
… components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We proved if vector fields are locally Lipschitz functions and satisfies quasi-positivity conditions, and if initial data are …
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Resonance Problems of the Fucik Spectrum Using Variational Methods
The Fucik spectrum of a linear operator, $L$, is defined to be the set,
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Variational Methods for p-Laplacian Sturm-Liouville Problems
In this work we address the problem of eigencurves for the p-Laplacian operator on [0,1]. First we examine the simple case where p=2. Next, we prove the existence and several properties of the first eigencurve and its corresponding eigenfunction. In chapters 4 and 5, the nonhomogeneous case is …
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… analysis are 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 …
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Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation
<p>Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the …
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Asymptotic staticity and tensor decompositions with fast decay conditions
… and Schoen, Chruściel and Delay have shown the existence of a large class of asymptotically flat vacuum initial data for Einstein's field equations which are static or stationary in a neighborhood of space-like infinity, yet quite general in the interior. The proof relies on some abstract, …
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An Optimal Control Approach to Implant Shape Design : Modeling, Analysis and Numerics
Facial trauma or congenital malformation of bones of the skull may degrade both skeletal integrity as well as the esthetic appearance. For the attending surgeon a prediction of the esthetic outcome of a bone replacement or augmentation implant insertion is challenging. Therefore, it would be …
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L² decay for weak solutions of the micropolar equations on R³
We obtain decay estimates for solutions of the micropolar fluid equations . Such equations, proposed by A. C. Eringen, generalize the classic model of Navier-Stokes and describe the behavior of fluids with microstructure such as animal blood, liquid crystals, suspensions, among others. For this, we …
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Backward stochastic Navier-Stokes equations in two dimensions
… part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is …
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Supercritical Semi-Linear Elliptic Problems Using Variational Principles
The thesis investigates the use of variational methods to study elliptic partial differential equations (PDEs) with supercritical nonlinearities. By focusing on convex subsets of a Banach space, the research overcomes compactness issues typically encountered with nonlinearities that exceed the …
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Monotone and pseudomonotone operators with applications to variational problems
… between Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone …
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SPDEs with Infinite-Variance Lévy Noise
This thesis is devoted to the study of the existence and uniqueness of solutions for stochastic partial differential equations (SPDEs) driven by Lévy noise. The main contributions of this work are contained in the recent publications [32] and [5]. Article [32] focuses on a stochastic wave equation …
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Global existence in L1 for the square-well kinetic equation
… equation, in order to model the kinetic theory of a moderately dense gas with intermolecular potential. The existence of solutions to the Cauchy problem in <i>L</i>¹. global in time and for arbitrary initial data. is proved. A simple derivation of the square-well kinetic equation is given. …
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Nonlinear Pseudoparabolic Equations and Variational Inequalities
The aim of this thesis is to prove existence and uniqueness of weak solutions for some types of quasilinear and nonlinear pseudoparabolic equations and for some types of quasilinear and nonlinear variational inequalities. The pseudoparabolic equations are characterized by the presence of mixed …
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Computer-assisted proofs in geometry and physics
… this dissertation we apply computer-assisted proof techniques to two problems, one in discrete geometry and one in celestial mechanics. Our main tool is an effective inverse function theorem which shows that, in favorable conditions, the existence of an approximate solution to a system of …
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Theory and Application of a Class of Abstract Differential-Algebraic Equations
We first provide a detailed background of a geometric projection methodology developed by Professor Roswitha Marz at Humboldt University in Berlin for showing uniqueness and existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic …
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Ricci Yang-Mills Flow
… to prove a non-collapsing theorem for certain solutions to Ricci Yang-Mills flow. We show that these equations, after an appropriate change of gauge, are equivalent to a strictly parabolic system, and hence prove general unique short-time existence of solutions. Furthermore we prove derivative …
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On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types
… domain optimization problems depends on the case of study. There are methods that have been developed for the discretized problem, but not much is done in the infinite dimensional case. We analyze the theoretical aspects of the infinite dimensional case for a particular domain optimization problem …
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