3 papers
math.AP2022
Regularity of Solutions for the Nonlocal Diffusion Equation on Periodic Distributions
Ilyas Mustapha, Bacim Alali, Nathan Albin
This work addresses the regularity of solutions for a nonlocal diffusion equation over the space of periodic distributions. The spatial operator for the nonlocal diffusion equation…
math.NA2019
Fourier spectral methods for nonlocal models
Bacim Alali, Nathan Albin
Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace o…
math.CA2018
Fourier multipliers for nonlocal Laplace operators
Bacim Alali, Nathan Albin
Fourier multiplier analysis is developed for nonlocal peridynamic-type Laplace operators, which are defined for scalar fields in . The Fourier multipliers are given t…