Sensitivity analysis for solutions to heterogeneous nonlocal systems

Abstract

The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous kernels that exhibit different types of weak singularities, space dependence, even regions of zero-interaction. The stability results showcase explicit bounds involving the measure of the domain and of the interaction collar size, nonlocal Poincar\'e constant, and other parameters. In the nonlinear setting the bounds quantify in different $L^p$ norms the sensitivity of solutions under different nonlinearity profiles. The results are validated by numerical simulations showcasing discontinuous solutions, varying horizons of interactions, and symmetric and heterogeneous kernels.