UMD空间中带分数阶导数的非自治演化方程的随机极大$L^p$-正则性
Stochastic maximal $L^p$-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces
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中文总结 AI 辅助
本文研究UMD空间中带广义分数阶导数的非自治随机演化方程的极大$L^p$-正则性，通过时间加权空间和正则-奇异分解获得适定性、时空正则性及随机极大$L^p$-正则性，并应用于非自治随机扩散方程和随机分数阶反应-扩散SIR模型。
中文摘要 AI 辅助
本文研究UMD空间中带广义分数阶导数的非自治随机演化方程的极大正则性理论。广义时间分数阶导数提供了一个统一框架，涵盖经典Riemann-Liouville和Caputo分数阶导数，从而适用于具有中间记忆效应的一类更广泛的异常扩散过程。基于初始项的奇异性和随机卷积核的奇异性，采用时间加权空间和正则-奇异分解来获得适定性、时空正则性和随机极大$L^p$-正则性结果。我们的结果应用于非自治随机扩散方程和随机分数阶反应-扩散SIR模型。
英文摘要
This paper is concerned with the maximal regularity theory for non-autonomous stochastic evolution equations with a generalized fractional derivative in UMD spaces. The generalized time-fractional derivative provides a unified framework covering both the classical Riemann-Liouville and Caputo fractional derivatives, which accommodates a wider class of anomalous diffusion processes with intermediate memory effects. Based on the singularities of the initial term and the stochastic convolution kernel, a time-weighted space and a regular-singular decomposition are used to obtain the well-posedness, space-time regularity, and stochastic maximal $L^p$-regularity results. Our results are applied to non-autonomous stochastic diffusion equation and stochastic fractional reaction-diffusion SIR model.
发表机构
- School of Mathematics, Guangxi University（广西大学数学学院）
- Guangxi Mathematical Research Center, Guangxi University（广西大学广西数学研究中心）
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