209 citations · 877 across the 58 of their papers we have counts for
59 papers
Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions
James M. Scott, Qiang Du
We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal…
Nonlocal problems with local boundary conditions I: function spaces and variational principles
James M. Scott, Qiang Du
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces a…
Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array
Qiang Du, Huaiyu Li, Michael Weinstein +1
We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dim…
Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing
Hoang Tran, Qiang Du, Guannan Zhang
We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is pr…
Bifurcation and fission in the liquid drop model: a phase-field approach
Zirui Xu, Qiang Du
The liquid drop model, originally used to model atomic nuclei, describes the competition between surface tension and Coulomb force. To help understand how a ball loses stability an…
Nonlocal boundary-value problems with local boundary conditions
James M. Scott, Qiang Du
We describe and analyze nonlocal integro-differential equations with classical local boundary conditions. The interaction kernel of the nonlocal operator has horizon parameter depe…