James H. Nolen
- Associate Professor of Mathematics
Research Areas and Keywords
PDE & Dynamical Systems
I study partial differential equations and probability, which have been used to model many phenomena in the natural sciences and engineering. In some cases, the parameters for a partial differential equation are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in differential equations modeling random phenomena and whether one can describe the statistical properties of solutions to these equations. Asymptotic analysis has been a common theme in much of my research. Current research interests include: reaction diffusion equations, homogenization of PDEs, stochastic dynamics, interacting particle systems.
Nolen, J, and Novikov, A. "Homogenization of the G-equation with incompressible random drift in two dimensions." Communications in Mathematical Sciences 9.2 (2011): 561-582.
Nolen, J, Xin, J, and Yu, Y. "Bounds on front speeds for inviscid and viscous G-equations." Methods and Applications of Analysis 16.4 (December 2009). (Academic Article)
Nolen, J, and Xin, J. "KPP Fronts in 1D Random Drift." Discrete and Continuous Dynamical Systems B 11.2 (2009). (Academic Article)
Nolen, J, and Ryzhik, L. "Traveling waves in a one-dimensional heterogeneous medium." Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis 26.3 (2009): 1021-1047. Full Text
Nolen, J, and Xin, J. "Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows." Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis 26.3 (2009): 815-839. Full Text
Nolen, J, and Papanicolaou, G. "Fine scale uncertainty in parameter estimation for elliptic equations." Inverse Problems 25.11 (2009). Full Text
Nolen, J, and Xin, J. "Variational principle and reaction-diffusion front speeds in random flows." ICIAM07-Proceedings (December 2008): 1040701-1040702. (Academic Article)
Nolen, J, Papanicolaou, G, and Pironneau, O. "A framework for adaptive multiscale methods for elliptic problems." Multiscale Modeling and Simulation 7.1 (2008): 171-196. Full Text