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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics

2017

University of Louisville

Articles 1 - 4 of 4

Full-Text Articles in Physical Sciences and Mathematics

Nonspreading Solutions In Integro-Difference Models With Allee And Overcompensation Effects., Garrett Luther Otto Dec 2017

Nonspreading Solutions In Integro-Difference Models With Allee And Overcompensation Effects., Garrett Luther Otto

Electronic Theses and Dissertations

Previous work in Integro-Difference models have generally considered Allee effects and over-compensation separately, and have either focused on bounded domain problems or asymptotic spreading results. Some recent results by Sullivan et al. (2017 PNAS 114(19), 5053-5058) combining Allee and over-compensation in an Integro-Difference framework have shown chaotic fluctuating spreading speeds. In this thesis, using a tractable parameterized growth function, we analytically demonstrate that when Allee and over-compensation are present solutions which persist but essentially remain in a compact domain exist. We investigate the stability of these solutions numerically. We also numerically demonstrate the existence of such solutions for more general …

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Regularized Solutions For Terminal Problems Of Parabolic Equations., Sujeewa Indika Hapuarachchi Aug 2017

Regularized Solutions For Terminal Problems Of Parabolic Equations., Sujeewa Indika Hapuarachchi

Electronic Theses and Dissertations

The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential equations (PDE) with terminal conditions are those in which the solution depends uniquely but not continuously on the given condition. In this dissertation, we explore how to find an approximation problem for a nonlinear heat equation which is well-posed. By using a small parameter, we construct an approximation problem and use a modified quasi-boundary value method to regularize a time dependent thermal conductivity heat equation and a quasi-boundary value method to regularize a space dependent thermal …

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Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., Heng Li Aug 2017

Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., Heng Li

Electronic Theses and Dissertations

Ductal carcinoma in situ (DCIS) is the earliest form of breast cancer. Three mathematical models in the one dimensional case arising from DCIS are proposed. The first two models are in the form of parabolic equation with initial and known moving boundaries. Direct and inverse problems are considered in model 1, existence and uniqueness are proved by using tool from heat potential theory and Volterra integral equations. Also, we discuss the direct problem and nonlocal problem of model 2, existence and uniqueness are proved. And approximation solution of these problems are implemented by Ritz-Galerkin method, which is the first attempt …

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Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King Aug 2017

Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King

Electronic Theses and Dissertations

In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. …

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