3 papers
math.AP2026
A Mountain-Pass Algorithm for Nonlocal Problems with Super-quadratic Nonlinearities
Loic Cappanera, Gabriela Jaramillo, Joshua M. Siktar
In this paper we consider a nonlinear equation with a super-quadratic nonlinearity, , and a nonlocal operator, , generated by a spe…
math.NA2025
The role of boundary constraints in simulating a nonlocal Gray-Scott model
Loic Cappanera, Gabriela Jaramillo
We present a second-order algorithm for approximating solutions to nonlocal diffusive processes in reaction-diffusion equations. The numerical scheme relies on a quadrature method…
math.NA2025
Artificial compressibility method for the incompressible Navier-Stokes equations with variable density
Cappanera Loic, Giordano Salvatore
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical vis…