报告题目：Random attractors for a stochastic nonlocal delayed reaction-diffusion equation on a semi-infinite interval

报告人：胡文杰 副编审（湖南师范大学）

邀请人：杨爽

报告时间：2026年9月21日19：30-20：30

报告地点：数学大楼912报告厅

参加人员：教师、研究生、本科生

报告摘要：In this talk,  we will study the existence and qualitative property of random attractors  for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition at the finite end. This equation models the spatial-temporal evolution of the mature individuals for a two-stage species whose juvenile and adults both diffuse that lives on a semi-infinite domain and subject to random perturbations. By transforming the SNDRDE into a random evolution equation with delay, we first establish the global existence and uniqueness of solutions to the equation, after which we show the solutions generate a random dynamical system. Then, we deduce uniform a priori estimates of the solutions and show the existence of bounded random absorbing sets. Subsequently, we prove the pullback asymptotic compactness of the random dynamical system generated by the SNDRDE with respect to the compact open topology, and hence obtain the existence of  random attractors. At last, it is proved that the random attractor is an exponentially attracting stationary solution under appropriate conditions. The theoretical results are demonstrated by application to the stochastic nonlocal delayed Nicholson's blowfly equation.

报告人简介：胡文杰，博士，副编审，湖南师范大学数学与统计学院硕士研究生导师，西班牙塞维利亚大学访问学者。主要研究领域为随机和无穷维动力系统理论及其在时滞方程中的应用，在Nonlinearity, J. Differential Equations，J. Dynam. Differential Equations等期刊发表论文 20 余篇。主持国家自然科学基金青年项目、中国博士后基金特等资助项目等各类科研项目7项，2025年入选湖南师范大学“世承人才计划”青年优秀人才。