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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
reaction-diffusion equations

Representative Publications
  1. J. Nolen, Normal approximation for a random elliptic equation, Probability Theory and Related Fields, vol. 159 no. 3 (2014), pp. 661-700 [pdf], [doi]
  2. J. Lu and J. Nolen, Reactive trajectories and the transition path process., Probability Theory and Related Fields (January, 2014) [1744], [doi]
  3. J. Nolen, A central limit theorem for pulled fronts in a random medium, Networks and Heterogeneous Media, vol. 6 no. 2 (2011), pp. 167-194 [pdf], [doi]
  4. J. Nolen and L. Ryzhik, Traveling waves in a one-dimensional heterogeneous medium, Annales de l'institut Henri Poincare -- Analyse Non Lineaire, vol. 26 no. 3 (2009), pp. 1021-1047 [pdf]
  5. A. Mellet, J. Nolen, J.-M. Roquejoffre, and L. Ryzhik, Stability of generalized transition fronts, Comm. PDE, vol. 34 no. 6 (2009), pp. 521-552 [pdf]
  6. J. Nolen and J. Xin, Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows, Annales de l'institut Henri Poincare -- Analyse Non Lineaire, vol. 26 no. 3 (2009), pp. 815-839 [pdf]
  7. P. Cardaliaguet, J. Nolen, P.E. Souganidis, Homogenization and enhancement for the G-equation, Archive for Rational Mechanics and Analysis, vol. 199 no. 2 (2011), pp. 527-561 [4160]

 

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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320