Nonlinear time-fractional subdiffusion-normal transport equations driven by stochastic noise on bounded domains

报告人：李诗琪

时间：2025-12-9 09:00-11:00am

地点：广西数学研究中心W301

摘要：In this paper, we investigate the initial value problem for a class of stochastic time-fractional subdiffusion-normal transport equations driven by additive noise on bounded domains. By utilizing resolvent operator theory and establishing refined estimates for the solution operators, we conduct a comprehensive analysis of the well-posedness of the problem. Specifically, under the Lipschitz assumption on the nonlinear source term, we employ the Picard iteration method and the fixed-point theorem to prove the global existence and uniqueness of mild solutions in the space of continuous functions. Furthermore, we investigate the regularity properties of the solution, which distinguishes this work from the deterministic case. By applying Itô isometry and fractional power operator estimates, we establish the spatial regularity in higher-order Sobolev spaces and the temporal Hölder continuity, revealing how the fractional operators smooth the roughness induced by the stochastic noise.