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Partial Differential Equations Commons™
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Articles 1 - 14 of 14
Full-Text Articles in Partial Differential Equations
Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox
Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox
University Honors Theses
A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic …
Hadamard Well-Posedness For Two Nonlinear Structure Acoustic Models, Andrew Becklin
Hadamard Well-Posedness For Two Nonlinear Structure Acoustic Models, Andrew Becklin
Department of Mathematics: Dissertations, Theses, and Student Research
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 }\Gamma_0\times(0,T),\\[1mm] \partial_\nu u=w_t&\text{ on }\Gamma\times(0,T),\\[1mm] w=\partial_{\nu_\Gamma}w=0&\text{ on }\partial\Gamma\times(0,T),\\[1mm] (u(0),u_t(0))=(u_0,u_1),\hspace{5mm}(w(0),w_t(0))=(w_0,w_1), \end{cases} \end{align*} where the initial data reside in the finite energy space, i.e., $$(u_0, u_1)\in H^1_{\Gamma_0}(\Omega) \times L^2(\Omega) \, \text{ …
Steady And Stable: Numerical Investigations Of Nonlinear Partial Differential Equations, R. Corban Harwood
Steady And Stable: Numerical Investigations Of Nonlinear Partial Differential Equations, R. Corban Harwood
Faculty Publications - Department of Mathematics
Excerpt: "Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation."
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Applications and Applied Mathematics: An International Journal (AAM)
In this article, modified (G'/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials.
4. Dragging Along, Ruth Dover
2. Population, Ruth Dover
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
3: Drugs And De's, Ruth Dover
3: Drugs And De's, Ruth Dover
Differential Equations
Making a connection between discrete recursion and differential equations.
1. Coffee, Ruth Dover
Stability Aware Delaunay Refinement, Bishal Acharya
Stability Aware Delaunay Refinement, Bishal Acharya
UNLV Theses, Dissertations, Professional Papers, and Capstones
Good quality meshes are extensively used for finding approximate solutions for partial differential equations for fluid flow in two dimensional surfaces. We present an overview of existing algorithms for refinement and generation of triangular meshes. We introduce the concept of node stability in the refinement of Delaunay triangulation. We present two algorithms for generating stable refinement of Delaunay triangulation. We also present an experimental investigation of a triangulation refinement algorithm based on the location of the center of gravity and the location of the center of circumcircle. The results show that the center of gravity based refinement is more effective …
Population Models, Jessica Hauer
Population Models, Jessica Hauer
EWU Masters Thesis Collection
This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in …
Parallel And Distributed Simulation Of Parabolic And Telegraphic Equations., Ewedafe Simon Uzezi
Parallel And Distributed Simulation Of Parabolic And Telegraphic Equations., Ewedafe Simon Uzezi
Student Works (2010-2019)
In this thesis, a parallel implementation of explicit/implicit parallel algorithms such as the stationary iterative methods and the class of iterating alternating methods which includes: Alternating Direction Implicit (ADI), Iterative Alternating Direction Explicit (IADE), for D’Yakonov (IADE-DY), Double sweep Mitchell and Fairweather (MF-DS) and Alternating Group Explicit (AGE) method for solving 1-Dimensional (1-D), 2-Dimensional (2-D) Parabolic (special examples including 1-D, 2-D Bio-Heat Equation) and 1-D, 2-D and 3-D Telegraphic Equations on a distributed environment of Message Passing Interface (MPI) and Parallel Virtual Machine (PVM) platform is presented. To correlate the communication activity with computation, we counted events between significant MPI/PVM …
Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe
Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe
Theses Digitization Project
This thesis studied the existence, uniqueness, and quenching behavior of the solution to a degenerate equation subject to the initial condition and the second boundary conditions.
The Motion Of A Thin Liquid Film Driven By Surfactant And Gravity, Michael Shearer, Rachel Levy
The Motion Of A Thin Liquid Film Driven By Surfactant And Gravity, Michael Shearer, Rachel Levy
All HMC Faculty Publications and Research
We investigate wave solutions of a lubrication model for surfactant-driven flow of a thin liquid film down an inclined plane. We model the flow in one space dimension with a system of nonlinear PDEs of mixed hyperbolic-parabolic type in which the effects of capillarity and surface diffusion are neglected. Numerical solutions reveal distinct patterns of waves that are described analytically by combinations of traveling waves, some with jumps in height and surfactant concentration gradient. The various waves and combinations are strikingly different from what is observed in the case of flow on a horizontal plane. Jump conditions admit new shock …
On Doubly Periodic Solutions Of Quasilinear Hyperbolic Equations Of The Fourth Order, T. Kiguradze, T. Smith
On Doubly Periodic Solutions Of Quasilinear Hyperbolic Equations Of The Fourth Order, T. Kiguradze, T. Smith
Publications
The problem on doubly periodic solutions is considered for a class of quasilinear hyperbolic equations. Effective sufficient conditions of solvability and unique solvability of this problem are established.