James H. Nolen
- Associate Professor of Mathematics
Research Areas and Keywords
PDE & Dynamical Systems
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. I also study the asymptotic behavior of stochastic processes.
Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields 159.3-4 (2014): 661-700. Full Text
Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields (2013): 1-40. Full Text
Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23 (2013): 2238-2258. (Academic Article) Full Text Open Access Copy
Nolen, J, Roquejoffre, J-M, Ryzhik, L, and Zlatoš, A. "Existence and Non-Existence of Fisher-KPP Transition Fronts." Archive for Rational Mechanics and Analysis 203.1 (2012): 217-246. Full Text
Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "A short proof of the logarithmic Bramson correction in Fisher-KPP equations (Accepted)." Networks and Heterogeneous Media (2012). (Academic Article)
Matic, I, and Nolen, J. "A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation." Journal of Statistical Physics 149.2 (2012): 342-361. Full Text
Cardaliaguet, P, Nolen, J, and Souganidis, PE. "Homogenization and Enhancement for the G-Equation." Archive for Rational Mechanics and Analysis 199.2 (2011): 527-561. Full Text
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. "An invariance principle for random traveling waves in one dimension." SIAM Journal on Mathematical Analysis 43.1 (2011): 153-188. Full Text