Sensitivity analysis for solutions to heterogeneous nonlocal systems

2021/09/13 by Nicole Buczkowski, Buczkowski, Nicole, Mikil Foss +5
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2109.06063

openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Poincaré 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.

Citations

• Reformulation of elasticity theory for discontinuities and long-range forces

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