Research Interests for James Nolen
Research Interests: Partial differential equations, stochastic processes, random media, applied mathematics, asymptotic analysis
I study partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. In many cases, the parameters for such equations are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in equations modeling random phenomena and whether one can describe the statistical properties of the solution to these equations. For example, I have worked on nonlinear partial differential equations that describe waves and moving interfaces in random media. This work involves ideas from both analysis and probability.  Areas of Interest:
partial differential equations stochastic processes asymptotic analysis homogenization theory front propagation reactiondiffusion equations
 Representative Publications
 J. Nolen and L. Ryzhik, Traveling waves in a onedimensional heterogeneous medium,
Annales de l'institut Henri Poincare  Analyse Non Lineaire, vol. 26 no. 3
(2009),
pp. 10211047 [pdf]
 A. Mellet, J. Nolen, J.M. Roquejoffre, and L. Ryzhik, Stability of generalized transition fronts,
Comm. PDE, vol. 34 no. 6
(2009),
pp. 521552 [pdf]
 J. Nolen and J. Xin, Asymptotic Spreading of KPP Reactive Fronts in Incompressible SpaceTime Random Flows,
Annales de l'institut Henri Poincare  Analyse Non Lineaire, vol. 26 no. 3
(2009),
pp. 815839 [pdf]
 J. Nolen, G. Papanicolaou, O. Pironneau, A Framework for Adaptive Multiscale Methods for Elliptic Problems,
SIAM Multiscale Modeling and Simulation, vol. 7
(2008),
pp. 171196, SIAM [pdf]
