Ryan Thompson

Associate Professor of Mathematics

Overview

Dr. Ryan Thompson joined the faculty of mathematics at UNG in the Fall of 2015. His current area of research lies in equations governing shallow water wave motion and answering fundamental questions such as existence and uniqueness of solutions, stability, continuity properties and spatial asymptotics. He has taught courses in calculus and the analysis of ordinary and partial differential equations. Dr. Thompson has also advised multiple senior projects in differential equations and the analysis of fluid motion.

Education

Ph.D., Mathematics, University of Notre Dame, 2015
M.S., Mathematics, University of Notre Dame, 2012
B.S., Mathematics, University of North Georgia, 2009

Research/Special Interests

Partial Differential Equations
- Fluid Dynamics
- Linear and Nonlinear Dispersive PDEs
- Linear and Nonlinear Evolution Equations

Publications

C. Thompson, The periodic Cauchy problem for the 2-component Camassa-Holm system, Differential and Integral Equations, 26 (2013), 155-182.
Himonas, R. C. Thompson, Persistence properties and unique continuation for a generalized Camassa-Holm equation, Journal of Mathematical Physics, 55 091503 (2014).
Holmes, R. C. Thompson, Classical Solutions to the Generalized Camassa-Holm Equation, Journal of Advances in Differential Equations, 22 No. 5-6, (2017), 339-362.
C. Thompson, Decay Properties of Solutions to a 4-parameter Family of Wave Equations, Journal of Mathematical Analysis and Applications, 451 (2017), 393-404.
Holmes, R. C. Thompson, Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces, Journal of Differential Equations, 263 No. 7 (2017), 4355-4381.