Browsing by Author "Shen, Wenxian"

Now showing items 1-19 of 19

A-Stability For Two Species Competition Diffusion Systems

Nguyen, Tung (2006-08-15)

My dissertation research focuses on establishing the structural stability of the attractor ($\mathcal{A}$-stability) via Morse-Smale property for diffusive two-species competition systems \begin{equation} \label{abst ...

Analysis and Optimal control of deterministic Vector-Borne diseases model

Son, Hyunjin (2018-07-18)

In this dissertation, two systems of deterministic differential equations are introduced to study the transmission of vector-borne diseases between a host and a vector. The total population of the host and the vector are ...

Dynamics of Chemotaxis Models in Heterogeneous Environments

Issa, Tahir Bachar (2019-06-07)

Chemotaxis describes the oriented movements of biological cells or organisms in response to chemical gradients in their environments and is crucial for many aspects of behaviour such as the location of food sources, ...

Global existence of classical solutions, spreading speeds, and traveling waves of chemotaxis models with logistic source on R^N

Salako, Rachidi Bolaji (2018-07-12)

This dissertation is devoted to the study of the classical Keller-Segel chemotaxis systems with space-time heterogeneous logistic source function on $R^N$. Chemotaxis systems are mathematical models describing aggregation ...

Global existence, persistence, spreading speeds, and forced waves in chemotaxis models

Xue, Shuwen (2021-07-29)

Chemotaxis models are widely used to describe the movements of biological species or living organisms in response to certain chemicals in their environments. This dissertation is devoted to the study of various dynamical ...

Hopfield Neural Lattice Models

Usman, Basiru (2020-07-22) ETD File Embargoed

Hopfield neural network model is a continuous deterministic model proposed by John J. Hopfield in the early 1980’s. The model was proposed in an attempt to produced an artificial neural network architecture that mimic ...

I-weight, special base properties and related covering properties

Bailey, Bradley (2005-12-15)

Alleche, Arhangel'ski\u{\i} and Calbrix defined the notion of a sharp base and posed the question: Is there a regular space with a sharp base whose product with [0, 1] does not have a sharp base? Chapter 2 contains an ...

Interior Backus Problem with Expanded Data

Zheng, Yuxiang (2019-12-09)

We consider a special formulation of the Backus geomagnetic problem in two and higher dimension. Given a domain $\Omega \subset \mathbb{R}^n$, we seek to determine whether there exists a unique harmonic function $u$ ...

Inverse source problem and inverse diffusion coefficient problem for parabolic equations with applications in geology

Ngoma, Sedar (2017-07-26)

This dissertation deals with inverse problems for parabolic partial differential equations with an integral constraint and their applications in geology. We employ analytical and numerical methods to analyze and approximate ...

The Lattice Gas Model and Lattice Boltzmann Model on Hexagonal Grids

Jin, Kang (2005-08-15)

We present an overview of the FHP model and the Lattice BGK model. Details regarding boundary conditions and initial conditions are discussed throught implementations on driven cavity flow, Poiseuille flow, and flow past ...

Nonlocal Dispersal Equations and Convergence to Random Dispersal Equations

Xie, Xiaoxia (2014-05-15)

This dissertation is devoted to the study of the dynamics of nonlocal and random dispersal evolution equations. Dispersal evolution equations are widely used to model the diffusions of organisms or individuals in many ...

Nonlocal Dispersal Equations with Almost Periodic Dependence

Onyido, Maria Amarakristi (2022-07-28)

Nonlocal dispersal equations are used to model the population dynamics of species that exhibit long-range dispersal mechanisms. This model of spatial spread is obtained by replacing the Laplacian in the usual reaction-diffusion ...

On The Lattice Boltzmann Method: Implementation and Applications

Jin, Kang (2008-12-15)

We studied the development and different types of the Lattice Boltzmann method. We gave several implementations. Then we presented two moving boundary treatments for the Lattice Boltzmann method, the second one is new. We ...

Parabolic-Elliptic Chemotaxis Models with Singular Sensitivity

Kurt, Halil Ibrahim (2022-07-25) ETD File Embargoed

Chemotaxis describes the movement of biological cells or organisms in response to certain chemicals in their environments and occupies an essential role in coordinating cell movement in many biological circumstances such ...

Principal Eigenvalue Theory for Time Periodic Nonlocal Dispersal Operators and Applications

Rawal, Nar (2014-07-02)

The dissertation is concerned with the spectral theory, in particular, the principal eigenvalue theory for nonlocal dispersal operators with time periodic dependence, and its applications. Nonlocal and random dispersal ...

Spatial Spread and Front Propagation Dynamics of Nonlocal Monostable Equations in Periodic Habitats

Zhang, Aijun (2011-07-25)

This dissertation is concerned with spatial spread and front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. Such equations arise in modeling the population dynamics ...

Spatial Spread Dynamics of Monostable Equations in Spatially Locally Inhomogeneous Media with Temporal Periodicity

Kong, Liang (2013-05-31)

This dissertation is devoted to the study of semilinear dispersal evolution equations. These type of equations are called as Monostable or KPP type equations, which arise in modeling the population dynamics of many ...

Stochastic Differential Equations: A Dynamical Systems Approach

Hollingsworth, Blane (2008-05-15)

The relatively new subject of stochastic differential equations has increasing impor- tance in both theory and applications. The subject draws upon two main sources, prob- ability/stochastic processes and differential ...

Transition Fronts in Time Heterogeneous Bistable Equations with Nonlocal Dispersal: Existence, Regularity, Stability and Uniqueness

Shen, Zhongwei (2015-04-30)

This dissertation is devoted to the existence, regularity, stability and uniqueness of transition fronts in nonlocal bistable equations in time heterogeneous media. Instead of existence, we start our study with ...