23 citations · 24 across the 4 of their papers we have counts for
5 papers
Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds
James Nolen, Matthew Rudd, Jack Xin
We prove the existence of Kolmogorov-Petrovsky-Piskunov (KPP) type traveling fronts in space-time periodic and mean zero incompressible advection, and establish a variational (mini…
Min-Max Variational Principle and Front Speeds in Random Shear Flows
James Nolen, Jack Xin
Speed ensemble of bistable (combustion) fronts in mean zero stationary Gaussian shear flows inside two and three dimensional channels is studied with a min-max variational principl…
Existence of KPP Type Fronts in Space-Time Periodic Shear Flows and a Study of Minimal Speeds Based on Variational Principle
James Nolen, Jack Xin
We prove the existence of reaction-diffusion traveling fronts in mean zero space-time periodic shear flows for nonnegative reactions including the classical KPP (Kolmogorov-Petrovs…
KPP Front Speeds in Random Shears and the Parabolic Anderson Problem
J. Xin
We study the asymptotics of front speeds of the reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity and zero mean stationary ergodic Gaussian shear a…
Self-Similar Decay in the Kraichnan Model of a Passive Scalar
G. Eyink, J. Xin
We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field, stationary and white-noise in time bu…