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 118 for “"Existence and uniqueness."”.
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Existence and uniqueness theorems for ordinary differential equations
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1959.
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Existence and uniqueness of best approximants, with numerical applications
Part I of the thesis deals with existence and uniqueness theorems. Strengthening a result due to J. Blatter, it is proved in chapter 3 that a normed linear space is complete if every closed, bounded, and convex set is proximinal. It is also shown, that in a semi-reflexive, locally convex, real …
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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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Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways
<p>In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential …
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Existence and Uniqueness of a solution to a flow problem about a Rotating Obstacle at low Reynolds number
… of angular momentum of the rigid body and the conservation of linear momentum of the fluid. When the conservation of angular momentum is taken into account, a dynamic boundary condition is considered. The uniqueness of this unknown velocity vector field is confirmed by using the so …
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Theory and Application of a Class of Abstract Differential-Algebraic Equations
… 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 aspects of this particular method, it can be extended to the case of infinite-dimensional abstract DAEs. For …
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A cholera model linking between-host, within-host and environmental disease dynamics
… are governed by human-human, environment-human, and within-human sub-dynamics. In this paper, a model is presented to incorporate all three of these dynamical components. The model is divided into three subgroups where the dynamics are analyzed according to their respective time scales. …
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Systemic Risk in Financial Networks
… mechanisms during fire sales, dynamic clearing and impact of contingent payments such as insurance and credit default swaps.</p>First, I present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. I demonstrate that the comonotonic setting …
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The discrete coagulation-fragmentation system
… 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 sequences. The theory of operator semigroups is then used to establish …
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Fractional Diffusion in Gaussian Noisy Environment
… are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness …
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Some Extensions of Poincaré-Bendixson Theory Applied to a Resonant Converter.
In this thesis existence and uniqueness of limit cycles are shown for a resonant converter, by extending Poincaré-Bendixson theory to non-smooth vector fields. We discuss relevant control theory and the role of simulations.
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Multi-scale and multi-group modeling techniques applied to Cholera and COVID-19
… are governed by human-human, environment-human, and within-human sub-dynamics. Specifically, the within-host dynamics incorporate virus and immune cell interaction with the vibrios. One model is presented to incorporate all three of these dynamical components. This model is extended to consider …
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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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Mixed variational problems associated with stationary viscous incompressible free boundary flows
… Ignore one of the boundary conditions at the FB and prove that for every chosen position of the FB the resultant problem, here called the auxiliary problem (AP), is well posed. (2) Establish regularity results for the solution of the AP. (3) Using (2) and the remaining boundary condition, …
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ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES
… to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators. The existence and uniqueness results for single term fractional differential equations (FDE) have also been established. We also obtain the Mellin transforms of such …
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Tribonacciho kód
… first derived using the <ling proof technique and subsequently with tools from discrete calculus. The text also addresses the existence and uniqueness of the Tribonacci representa<on.
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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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STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION AND THEIR GENERALIZATIONS
… motion with Hurst parameter $H>1/2$. We prove an existence and uniqueness result of the solution to the stochastic differential equation. We investigate the dependence of the solution on the initial condition and the existence of finite moments of the solution. Furthermore we generalize these …
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Circle Packing in Euclidean and Hyperbolic Geometries
… that the vertices represent centers of circles, and the edges denote patterns of tangency. Such a configuration of circles is called a circle packing. We shall give evidence for the existence and uniqueness of circle packings generated by such graphs, as well as an explanation of the algorithms …
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