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 27 for “"existence and uniqueness of solutions"”.
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Existence and uniqueness of solutions of boundary value problems by matching solutions.
In this dissertation, we investigate the existence and uniqueness of boundary value problems for the third and nth order differential equations by matching solutions. Essentially, we consider the interval [a, c] of a BVP as the union of the two intervals [a, b] and [b, c], analyze the solutions of …
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Nonlinear neutral functional differential equations in product spaces
… equations in product spaces. At this point existence and uniqueness of solutions are studied. This formulation is used to develop a general approximation scheme for those systems. Convergence of this scheme is analyzed. It is also shown how spline based approximating methods fall within this …
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Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation
This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of …
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The discrete coagulation-fragmentation system
In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of …
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Estudo da estabilidade de circuitos RC via otimização
Study of non-linear RC network stability. An RC network is considered assymptotically stable when the capacitar charges converge to equilibrium charges. The study is developed from the analysis of the behavior of resistive networks. It is assumed that all resistors have increasing characteristics …
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Constrained signal reconstruction
… this dissertation addresses the reconstruction of signals and images from linear measurements subject to convex constraints. The objectives are to describe the existence and uniqueness of solutions, to characterize reconstructions, and to develop algorithms for efficiently computing …
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Degree Theory and Nonlinear Boundary Value Problems at Resonance
… L}y$ = Ly + $\eta y\sp3$, where $\eta$ = $\pm$1 and L, the linear part of ${\cal L}$, is of the form Ly = $y\sp{\prime\prime}$ + $p(x)y\sp\prime$ + q(x)y. Assume p(x) and q(x) are integrable on (a,b). We study the existence and uniqueness of solutions of ${\cal L}y$ = f satisfying linear boundary …
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Mixed methods and reduced integration for the circular arch problem
… The problem is formulated in both the standard and mixed variational forms which include a parameter relating to the thickness of the arch. Existence and uniqueness of solutions to these equivalent problems is established and the corresponding discrete problems are studied. Finite element …
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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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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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Taming of Complex Dynamical Systems
The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential …
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Critical perturbations of elliptic operators by lower order terms
In this work we study issues of existence and uniqueness of solutions of certain boundary value problems for elliptic equations in the upper half-space. More specifically we treat the Dirichlet, Neumann, and Regularity problems for the general second order, linear, elliptic operator under a …
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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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Computational Methods for Feedback Control in Structural Systems
… methods, LQR control, an abstract formulation andreduced basis techniques for a system consisting of a thin cylindrical shellwith surface-mounted piezoceramic actuators are investigated.Donnell-Mushtari equations,modified to include Kelvin-Voigt damping and passive patch contributions,are used …
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Mathematical Models of Prevascular Tumor Growth by Diffusion
<p>A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly …
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Existence and stability of solutions to the equations of fibre suspension flows
… in an averaged sense, through the introduction of a second-order orientation tensor A. This variable, together with the velocity and pressure, then constitutes the set of unknown variables for the problem. The governing equations are balance of linear momentum, the incompressibility condition, …
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Nonlinear scale space analysis in image processing
The objective of this work is to develop and analyze robust and fast image segmentation algorithms. They must be robust to pervasive, large-amplitude noise, which cannot be well characterized in terms of probabilistic distributions. This is because the applications of interest include synthetic …
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Analysis, finite element approximation, and computation of optimal and feedback flow control problems
The analysis, finite element approximation, and numerical simulation of some control problems associated with fluid flows are considered. First, we consider a coupled solid/fluid temperature control problem. This optimization problem is motivated by the desire to remove temperature peaks, i.e., …
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Benzene and Its Effect on Erythropoiesis: Models, Optimal Controls, and Analyses
… presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain. The exposure-dose-response …
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