The research activity in differential equations at CSU includes both ordinary and partial differential equations and embraces numerical/computational as well as theoretical investigations. There is considerable activity in the area of dynamical systems, particularly in the study of instabilities and pattern formation with applications to pattern analysis and neural networks. This activity is leading to increasing collaboration (in the form of joint seminars and cooperative degree programs etc.) with various departments of biological sciences on campus.
Research activity in partial differential equations includes such topics as: new techniques for a posteriori error analysis for finite element solutions of elliptic boundary value problems, computational fluid dynamics, vector algorithms and numerical methods for conservation laws, reconstruction algorithms for electrical impedance tomography (EIT), as well as direct and inverse problems associated with flow in porous media, including modelling of contaminant transport in groundwater. These efforts have led to cooperative links with various engineering departments and with soil physicists in the agronomy department.
The following faculty members have research interests in Differential Equations.
Inverse Problems, Radar Imaging
Dynamical Systems and Applications
Partial differential equations, optimal control, inverse problems
Inverse problems, electrical impedance tomography, medical imaging, PDE's
Dynamical systems; pattern formation; fluid dynamics, hydrodynamic and hydromagnetic stability and bifurcation; numerical analysis; mathematical modeling
Partial Differential Equations, Waves in Random Media, Inverse Problems, Quantum Transport
Statistical Signal Processing , Wireless Communication
Differential Equations, Mathematical Biology, Applied Math
Multi-physics and multi-scale problems; numerical solution, sensitivities and parametrization
Theoretical Ecology and Evolution
Numerical Methods for PDEs, Mathematical Biology, Fluid Dynamics