Hassan Allouba : Time-fractional and L-Kuramoto-Sivashinsky (S)PDEs: two sides of the Brownian-time coin

Posted by Cheng Ouyang , part of the Statistics and Data Science Seminar.

At

Oct. 21, 2015, 4 p.m.

In

SEO 636

Abstract

High order and fractional PDEs have become prominent in theory and in modeling many phenomena. We introduce two large classes of time-fractional and fourth order L-Kuramoto-Sivashinsky (L-KS) Stochastic PDEs. The L-KS PDE/SPDE class is connected to many pattern-formation phenomena. The latter class of time-fractional stochastic equations is related to noisy slow diffusion or diffusion in material with memory. We give comprehensive, sharp, and dimension-dependent Holder and modulus of continuity regularity results for both classes. One important theme of this talk—which is based on a series of our papers—is on the key role Brownian-time processes, their extensions, and their associated kernels play in giving a unifying explicit formulation and in capturing precise behaviors of these two important classes.