My Ph.D. dissertation concerned decay properties of solutions to the Benjamin-Ono IVP on weighted Sobolev spaces. My research interests involve KdV-like dispersive equations, their unique continuation properties, and more recently, questions related to control and stabilization of these equations on a periodic domain.
When I'm not working on PDEs, I also enjoy research investigations that involve undergraduate and masters students. We explore topics in PDEs, harmonic analysis, measure theory, numerical analysis, optimization, linear algebra and recently, classification problems in machine learning.
C. Flores. Control and stability of the linearized dispersion-generalized Benjamin-Ono equation on a periodic domain -- Math. Control Signals Syst. (2018) 30: 13. https://doi.org/10.1007/s00498-018-0219-z
C. Flores, D.L. Smith, S. Oh. Stabilization of dispersion-generalized Benjamin-Ono equation. arXiv:1709.10224 -- accepted
C. Flores, D.L. Smith. Control and stabilization of periodic fifth-order Korteweg-de Vries equation. arXiv:1706.04798 -- published
C. Flores. On decay properties of solutions to the IVP for the Benjamin-Ono equation. J Dyn Diff Equat (2013) 25: 907. https://doi.org/10.1007/s10884-013-9321-6
Past Research Projects with Students, Faculty collaborations, and Community Partnerships
Moment Problems and Applications to PDEs
Numerical Methods, Simulations, and Control of Traffic Flow in Ventura County
An epidemiological math modeling approach for Voter Dynamics -- collaboration with Dr. S. Banuelos and inspired by the Ventura County non-profit CAUSE, to appear in CODEE
Topics in dispersive PDEs with Math Master's students.
Data Projects for Ventura County Public Health -- collaboration with Dr. A. Kryshchencko (results coming soon!)
I enjoyed visiting the Universidad Autonoma del Estado de Hidalgo in Pachuca, Mexico in November 2018 for the 14 Annual Analysis & Mathematical Physics Symposium. I was able to share my control theory results; you may enjoy reading this brief article about the meeting.
