Computation, Analysis and Applications of PDEs with Nonlocal and Singular Operators

Overview

Many physical phenomena and engineering processes involve nonlocal diffusion or global interactions, but their effective modeling, simulation and mathematical justification can be difficult. Partial different equations (PDEs) with nonlocal and singular operators, which particularly include fractional derivatives, fractional or nonlocal Laplacian and convolutions, have been emerging as a powerful tool for modelling overlapping microscopic and macroscopic scales, anomalous diffusion/transport, anisotropic dispersive media, long-range time memory or spatial interactions and among others. In the past decade, there has been much progress in both modelling and computation related to this subject area.