发表机构
School of Mathematics, Shandong University; Geotechnical and Structural Engineering Research Center, Shandong University（山东大学数学学院; 山东大学岩土结构工程研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对由分形高斯噪声驱动的随机多尺度次扩散模型，采用解算子方法与扰动技术证明其温和解的适定性，提出两类数值格式并验证收敛速率，通过实验支撑理论结果。
AI 中文摘要
本文研究由分形高斯噪声驱动的随机多尺度次扩散模型，其中采用带可变指数α(t)∈(0,1)的多尺度Abel核来捕捉反常扩散中的多尺度与交叉行为。该模型的主要难点在于多尺度Abel核的复杂性（如非单调性和非强制性）以及噪声导致的低正则性。针对这些问题，本文通过解算子方法和多尺度Abel核的扰动技术，证明了温和解的适定性与正则性；随后在低正则性数值分析框架下，提出并分析了半离散时间和全离散数值格式，证明了其时间与空间收敛速率；最后通过数值实验验证了理论结果。
英文摘要
This paper investigates a stochastic multiscale subdiffusion model driven by fractional Gaussian noise, where the multiscale Abel kernel with variable exponent $α(t)\in(0,1)$ is used to capture multiscale and crossover behavior in anomalous diffusion. The main difficulties of this model lie in the complexity of the multiscale Abel kernel (e.g. non-monotonicity and non-coercivity) and the low regularity caused by the noise. Concerning these issues, we prove the well-posedness and regularity of the mild solutions by means of solution operator approach and a perturbation technique for multiscale Abel kernel. Then both the semidiscrete-in-time and fully-discrete numerical schemes are proposed and analyzed under the low-regularity numerical analysis framework, with proved temporal and spatial convergence rates. Numerical experiments are presented to substantiate the theoretical results.
