3 papers
math.NA2026
Discontinuity Analysis and Semi-Analytic Spectral Approximation for the Nonlocal Poisson Equation
Thinh Dang, Bacim Alali, Nathan Albin
We study a nonlocal Poisson problem with discontinuous source term and analyze how the regularity of the integral kernel determines the discontinuity structure of the corresponding…
math.AP2024
Regularity of Solutions for Peridynamics Equilibrium and Evolution Equations on Periodic Distributions
Thinh Dang, Bacim Alali, Nathan Albin
Results on the peridynamics equilibrium and evolution equations over the space of periodic vector-distributions in multi-spatial dimensions are presented. The associated operator c…
math.AP2024
Regularity of Solutions for the Nonlocal Wave Equation on Periodic Distributions
Thinh Dang, Bacim Alali, Nathan Albin
This work addresses the regularity of solutions for a nonlocal wave equation over the space of periodic distributions. The spatial operator for the nonlocal wave equation is given…