Term of Award

Spring 2019

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Dr Shijun Zheng

Committee Member 1

Dr Yongki Lee

Committee Member 2

Dr Martha Abell

Committee Member 3

Dr Yi Hu

Abstract

In this thesis, we present a twofold work, a survey of existing results on Scattering for Magnetic Nonlinear Schrodinger equation (mNLS) in 3-D and a class of Non-local Conservation laws. We provided detailed steps to formulate the compressible Euler equation from which the Virial Identity is derived. We discussed the local, global existence results and scattering where the Morawetz type estimates relies on the virial identity and we used other estimate types and some sense of Sobolev embedding. We also considered a non-local traffic flow model with Arrhenius look ahead dynamics. Though a conventional numerical approximation scheme may lead to the breakdown of the maximum principle, we construct Maximum-Principle-Satisfying numerical schemes for a class of non-local conservation laws and display numerical simulations of traffic flow models. The techniques and ideas developed in this work are applicable to a large class of non-local conservation laws.

Research Data and Supplementary Material

Yes

Available for download on Tuesday, April 16, 2024

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