Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Mathematical Sciences
Dr Shijun Zheng
Committee Member 1
Dr Yongki Lee
Committee Member 2
Dr Martha Abell
Committee Member 3
Dr Yi Hu
Committee Member 3 Email
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.
Farotimi, Oluwaseun P., "Survey of Results on Scattering for Magnetic Nonlinear Schrödinger Equation in 3-D and a Class of Nonlocal Conservation Laws" (2019). Electronic Theses and Dissertations. 1924.
Research Data and Supplementary Material
Available for download on Tuesday, April 16, 2024