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You searched for +publisher:"University of Louisville" +contributor:("Swanson, David"). Showing records 1 – 2 of 2 total matches.

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University of Louisville

1. Hapuarachchi, Sujeewa Indika. Regularized solutions for terminal problems of parabolic equations.

Degree: PhD, 2017, University of Louisville

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 conductivity heat equation. Finally we prove, in both cases, the approximation solution converges to the original solution whenever the parameter goes to zero. Advisors/Committee Members: Xu, Yongzhi, Swanson, David, Hu, Changbing, Gie, Gung-Min, Sumanasekera, Gamini.

Subjects/Keywords: partial differential equation; sobolev space; regularization; Partial Differential Equations

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APA (6th Edition):

Hapuarachchi, S. I. (2017). Regularized solutions for terminal problems of parabolic equations. (Doctoral Dissertation). University of Louisville. Retrieved from 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

Chicago Manual of Style (16th Edition):

Hapuarachchi, Sujeewa Indika. “Regularized solutions for terminal problems of parabolic equations.” 2017. Doctoral Dissertation, University of Louisville. Accessed June 26, 2019. 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776.

MLA Handbook (7th Edition):

Hapuarachchi, Sujeewa Indika. “Regularized solutions for terminal problems of parabolic equations.” 2017. Web. 26 Jun 2019.

Vancouver:

Hapuarachchi SI. Regularized solutions for terminal problems of parabolic equations. [Internet] [Doctoral dissertation]. University of Louisville; 2017. [cited 2019 Jun 26]. Available from: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776.

Council of Science Editors:

Hapuarachchi SI. Regularized solutions for terminal problems of parabolic equations. [Doctoral Dissertation]. University of Louisville; 2017. Available from: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776


University of Louisville

2. Otto, Garrett Luther. Nonspreading solutions in integro-difference models with allee and overcompensation effects.

Degree: PhD, 2017, University of Louisville

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 growth functions. Advisors/Committee Members: Li, Bingtuan, Emery, Sarah, Emery, Sarah, Gie, Gung-Min, Hu, Changbing, Swanson, David.

Subjects/Keywords: mathematical biology; integrodifference equation; Allee effect; overcompensation; spatial population ecology; Applied Mathematics; Dynamic Systems; Population Biology

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Otto, G. L. (2017). Nonspreading solutions in integro-difference models with allee and overcompensation effects. (Doctoral Dissertation). University of Louisville. Retrieved from 10.18297/etd/2858 ; https://ir.library.louisville.edu/etd/2858

Chicago Manual of Style (16th Edition):

Otto, Garrett Luther. “Nonspreading solutions in integro-difference models with allee and overcompensation effects.” 2017. Doctoral Dissertation, University of Louisville. Accessed June 26, 2019. 10.18297/etd/2858 ; https://ir.library.louisville.edu/etd/2858.

MLA Handbook (7th Edition):

Otto, Garrett Luther. “Nonspreading solutions in integro-difference models with allee and overcompensation effects.” 2017. Web. 26 Jun 2019.

Vancouver:

Otto GL. Nonspreading solutions in integro-difference models with allee and overcompensation effects. [Internet] [Doctoral dissertation]. University of Louisville; 2017. [cited 2019 Jun 26]. Available from: 10.18297/etd/2858 ; https://ir.library.louisville.edu/etd/2858.

Council of Science Editors:

Otto GL. Nonspreading solutions in integro-difference models with allee and overcompensation effects. [Doctoral Dissertation]. University of Louisville; 2017. Available from: 10.18297/etd/2858 ; https://ir.library.louisville.edu/etd/2858

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