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All Articles in Partial Differential Equations

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593 full-text articles. Page 1 of 21.

Spreading Mechanics And Differentiation Of Astrocytes During Retinal Development, Tracy Stepien, Timothy W. Secomb 2020 University of Florida

Spreading Mechanics And Differentiation Of Astrocytes During Retinal Development, Tracy Stepien, Timothy W. Secomb

Biology and Medicine Through Mathematics Conference

No abstract provided.


Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell 2020 Nova Southeastern University

Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell

Biology and Medicine Through Mathematics Conference

No abstract provided.


Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, Yirui Chen 2020 Virginia Polytechnic Institute and State University

Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, Yirui Chen

Biology and Medicine Through Mathematics Conference

No abstract provided.


Parameter Estimation For Tear Film Thinning, Rayanne Luke 2020 University of Delaware

Parameter Estimation For Tear Film Thinning, Rayanne Luke

Biology and Medicine Through Mathematics Conference

No abstract provided.


Hadamard Well-Posedness For Two Nonlinear Structure Acoustic Models, Andrew Becklin 2020 University of Nebraska - Lincoln

Hadamard Well-Posedness For Two Nonlinear Structure Acoustic Models, Andrew Becklin

Dissertations, Theses, and Student Research Papers in Mathematics

This dissertation focuses on the Hadamard well-posedness of two nonlinear structure acoustic models, each consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ strongly coupled with a Berger plate equation acting only on a flat portion of the boundary of $\Omega$. In each case, the PDE is of the following form: \begin{align*} \begin{cases} u_{tt}-\Delta u +g_1(u_t)=f(u) &\text{ in } \Omega \times (0,T),\\[1mm] w_{tt}+\Delta^2w+g_2(w_t)+u_t|_{\Gamma}=h(w)&\text{ in }\Gamma\times(0,T),\\[1mm] u=0&\text{ on ...


Non-Linear Modifications Of Black-Scholes Pricing Model With Diminishing Marginal Transaction Cost, Kaidi Wang 2020 William & Mary

Non-Linear Modifications Of Black-Scholes Pricing Model With Diminishing Marginal Transaction Cost, Kaidi Wang

Undergraduate Honors Theses

In the field of quantitative financial analysis, the Black-Scholes Model has exerted significant influence on the booming of options trading strategies. Publishing in their Nobel Prize Work in 1973, the model was generated by Black and Scholes. Using Ito’s Lemma and portfolio management methodology, they employed partial differential equation to provide a theoretical estimate of the price of European-style options.

This paper is interested in deriving non-linear modifications of the Black-Scholes model with diminishing marginal transaction cost.


483— Effectiveness Of Mmr Vaccination In Orthodox Jewish Neighborhoods, Meenu Mundackal 2020 SUNY Geneseo

483— Effectiveness Of Mmr Vaccination In Orthodox Jewish Neighborhoods, Meenu Mundackal

GREAT Day

Measles is a highly contagious disease, where large outbreaks arise by direct contact between susceptible (unvaccinated) and infectious individuals. Many Orthodox Jewish neighborhoods were affected by measles from 2018-2019. To quantify the vaccination effort on this susceptible population, a retrospective analysis was used to study the NYC and Rockland County populations using a differential equations model. A subsequent model, known as a realistically-structured network model, studied only the NYC population, in relation to typical household size. Vaccination strategies were applied to three cohorts: unvaccinated family members, members with 1 prior MMR dose, and members with 2 prior MMR doses. The ...


A Time Integration Method Of Approximate Particular Solutions For Nonlinear Ordinary Differential Equations, Cyril Ocloo 2020 The University of Southern Mississippi

A Time Integration Method Of Approximate Particular Solutions For Nonlinear Ordinary Differential Equations, Cyril Ocloo

Master's Theses

We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration method. The superposition principle is applied to split the numerical solution at each time step into an approximate particular solution and a homogeneous solution. Delta-shaped basis functions are used to provide an approximation of the source function at each time step. The purpose of this is to ...


Numerical Analysis Of Three-Dimensional Mhd Flow Of Casson Nanofluid Past An Exponentially Stretching Sheet, Madhusudan Senapati, Kharabela Swain, Sampad Kumar Parida 2020 S 'O' A Deemed to be University

Numerical Analysis Of Three-Dimensional Mhd Flow Of Casson Nanofluid Past An Exponentially Stretching Sheet, Madhusudan Senapati, Kharabela Swain, Sampad Kumar Parida

Karbala International Journal of Modern Science

The convective three dimensional electrically conducting Casson nanofluid flow over an exponentially stretching sheet embedded in a saturated porous medium and subjected to thermal as well as solutal slip in the presence of externally applied transverse magnetic field (force-at-a-distance) is studied. The heat transfer phenomenon includes the viscous dissipation, Joulian dissipation, thermal radiation, contribution of nanofluidity and temperature dependent volumetric heat source. The study of mass diffusion in the presence of chemically reactive species enriches the analysis. The numerical solutions of coupled nonlinear governing equations bring some earlier reported results as particular cases providing a testimony of validation of the ...


Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva 2020 Scientific and Innovation Center of Information and Communication Technologies at Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Address: Amir Temur street, 108, 100200, Tashkent city, Republic of Uzbekistan

Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva

Chemical Technology, Control and Management

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an ...


Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze 2020 Technological University Dublin

Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze

Articles

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and ...


A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang 2020 Southern Methodist University

A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang

Mathematics Theses and Dissertations

Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating ...


Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi 2019 The University of Western Ontario

Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi

Electronic Thesis and Dissertation Repository

Differential Equations are used to mathematically express the laws of physics and models in biology, finance, and many other fields. Examining the solutions of related differential equation systems helps to gain insights into the phenomena described by the differential equations. However, finding exact solutions of differential equations can be extremely difficult and is often impossible. A common approach to addressing this problem is to analyze solutions of differential equations by using their symmetries. In this thesis, we develop algorithms based on analyzing infinitesimal symmetry features of differential equations to determine the existence of invertible mappings of less tractable systems of ...


Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King 2019 Chapman University

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also ...


Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker 2019 CUNY New York City College of Technology

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

Publications and Research

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.


Multi-Point Flux Approximations Via The O-Method, Christen Leggett 2019 University of Southern Mississippi

Multi-Point Flux Approximations Via The O-Method, Christen Leggett

Master's Theses

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients ...


Analyzing Student Loan Debt Using Seir Compartmental Model Of Epidemiology, Kavya Ravishankar, Dr. Padmanabhan Seshaiyer 2019 George Mason University

Analyzing Student Loan Debt Using Seir Compartmental Model Of Epidemiology, Kavya Ravishankar, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Sperm Motility In Groups, Julie Simons 2019 California State University Maritime Academy

Sperm Motility In Groups, Julie Simons

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer 2019 George Mason University

Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Asymptotics Of Solutions And Numerical Simulation Of The Nonlinear Heat Conductivity Problem With Absorption And Variable Density, Mersaid Aripov, Askar Mukimov 2019 National University of Uzbekistan

Asymptotics Of Solutions And Numerical Simulation Of The Nonlinear Heat Conductivity Problem With Absorption And Variable Density, Mersaid Aripov, Askar Mukimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present work, the asymptotic behavior of the solutions of the nonlinear variable-density thermal conductivity problem with absorption is obtained. The critical value parameter is considered. The resulting asymptotics was used as an initial approximation, numerical calculations were performed. As a difference scheme, a three-layer difference scheme was used, which, unlike a two-layer scheme, has greater accuracy.


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