Research in Differential Equations

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.

Margaret Cheney

Inverse Problems, Radar Imaging

Gerhard Dangelmayr

Dynamical Systems and Applications

Oleg Emanouilov

Partial differential equations, optimal control, inverse problems

Jennifer Mueller

Inverse problems, electrical impedance tomography, medical imaging, PDE's

Iuliana Oprea

Dynamical systems; pattern formation; fluid dynamics,  hydrodynamic and hydromagnetic stability and bifurcation; numerical analysis; mathematical modeling

Olivier Pinaud

Partial Differential Equations, Waves in Random Media, Inverse Problems, Quantum Transport

Louis Scharf

Statistical Signal Processing , Wireless Communication

Patrick Shipman

Differential Equations, Mathematical Biology, Applied Math

Simon Tavener

Multi-physics and multi-scale problems; numerical solution, sensitivities and parametrization

Colleen Webb

Theoretical Ecology and Evolution

Yongcheng Zhou

Numerical Methods for PDEs, Mathematical Biology, Fluid Dynamics