理学院学术报告—Invariant manifolds for a randomly perturbed non-autonomous coupled system and their approximations

报告题目：Invariant manifolds for a randomly perturbed non-autonomous coupled system and their approximations

报 告 人：申俊

报告时间：2023年11月29日10：30—12：00

报告地点：2B-409

报告内容： In this talk we consider long time dynamics of a randomly perturbed non-autonomous coupled system , whose  coordinate satisfies a semilinear parabolic equation with an additive noise, and  coordinate satisfies a differential equation whose solutions do not converge too rapidly. The noise is either the white noise induced by a Brownian motion  or a stationary process whose integral is approximating . After addressing certain assumptions for such system, we show that for (resp. ) with respect to the noise  (resp. integral of  there exists a invariant manifold which is exponentially attracting any other solution outside it. Also, as  tends to 0, the invariant manifold and its derivative in  for the case  are approaching to those for .

报告人简介：申俊，四川大学副教授，博士生导师, 四川省学术和技术带头人后备人选；曾在英国伦敦帝国理工学院、美国杨百翰大学访问；现主持国家自然科学基金面上项目1项，参加国家重大、重点项目各1项；在《Journal of Differential Equations》、《Journal of Dynamics and Differential Equations》、《Discrete and Continuous Dynamical Systems-Series A》、《SCIENCE CHINA Mathematics》、《Physica D》等上面发表文章数篇。