On some nonlocal, nonlinear diffusion problems

TL;DR

This paper investigates nonlocal, nonlinear elliptic problems, focusing on solution computation via fixed point methods, and provides error estimates along with numerical experiments to validate the approach.

Contribution

It introduces a fixed point framework for solving nonlocal, nonlinear elliptic problems and offers error analysis and numerical validation.

Findings

Effective fixed point method for solution computation

Error estimates for the numerical approach

Numerical experiments demonstrating method validity

Abstract

This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments are provided.