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 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.
| Original language | English |
|---|---|
| Pages (from-to) | 367-397 |
| Number of pages | 31 |
| Journal | Journal of Peridynamics and Nonlocal Modeling |
| Volume | 4 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2022 |
| Externally published | Yes |
Funding
MLP was supported by the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under the Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US Department of Energy or the US Government. MLP was supported by the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under the Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US Department of Energy or the US Government.
| Funders | Funder number |
|---|---|
| U.S. Department of Energy | |
| Office of Science | |
| National Nuclear Security Administration | DE-NA0003525 |
| Advanced Scientific Computing Research | |
| Government of South Australia |
Keywords
- Heterogeneous kernels
- Integrable kernels
- Nonlocal systems
- Numerical studies
- Sensitivity analysis