Ryan Thompson, Ph.D.
Overview
Dr. Ryan Thompson joined the faculty of mathematics at 91ÁÔÆæ 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
Selected Publications
- R. 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).
- J. 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.
- J. Holmes, R. C. Thompson, F. Tiğlay, The Cauchy Problem for the Gurevich-Zybin System, Journal of Mathematical Physics, 63, No. 4 (2022).