Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies
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. Here, 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 Lp 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.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- NA0003525
- OSTI ID:
- 1887420
- Report Number(s):
- SAND2022-12266J; 709750
- Journal Information:
- Journal of Peridynamics and Nonlocal Modeling, Vol. 4, Issue 3; ISSN 2522-896X
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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