Nonlinear Ayalysis
Our research focuses on the mathematical structure of systems described by nonlinear partial differential equations.
Nonlinear analysis focusing on reaction-diffusion equations
We are researching qualitative theory for nonlinear partial differential equations, such as elliptic and parabolic equations, and systems of ordinary differential equations, which are related to various phenomena. We are interested in methods that use general theory such as functional analysis, as well as individual methods, with a focus on frameworks such as eigenvalue problems and variational methods.
Qualitative theory of reaction-diffusion models with logistic growth
This research originated with the analysis by John Gordon Skellam, a statistician and ecologist, of the data on the expansion of the distribution range of the European muskrat, using reaction-diffusion equations with a logistic-type nonlinear term to show that the rate of expansion of the distribution range was almost constant. In terms of models for the population dynamics of a single species, we are interested in and researching the properties of reaction-diffusion equations when viewed macroscopically.
Analysis of nonlinear simultaneous differential equations on network graphs
Our research is focused on the influence of the topology of network graphs on the properties of simultaneous ordinary differential equations. In particular, we are analyzing the properties of equations that appear in multi-patch models, which are models of population dynamics that treat populations as groups of individuals called “patches”.