Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies
Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies
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异构非局部系统解决方案的敏感性分析。理论和数值研究
DOI：
10.1007/s42102-022-00081-6
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Radu, Petronela
中科院分区：
文献类型：
--
作者：
Buczkowski, Nicole E.;Foss, Mikil D.;Parks, Michael L.;Radu, Petronela
本文提出了一个收集的结果连续依赖的数据和系统参数扰动下的非局部问题的解决方案。出现在系统中的积分算子通过表现出不同类型的弱奇异性，空间依赖性，甚至零相互作用区域的异构内核捕获相互作用。的稳定性结果显示明确的界限，涉及的测量域和相互作用的衣领的大小，非本地庞加莱常数，和其他参数。在非线性环境下，边界以不同的范数量化了不同非线性曲线下解的灵敏度。数值模拟展示不连续的解决方案，不同的视野的相互作用，对称和异构内核的结果进行了验证。
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 differentnorms 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.