Sensitivity analysis for solutions to heterogeneous nonlocal systems
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,...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2109.06063 |