活动时间：2026-07-14 15:00
活动地点：2号学院楼2432
主讲人：杨小青
主讲人中文简介：
杨小青，兰州大学博士研究生（巴西圣保罗大学联合培养），主要研究无穷维动力系统的长时间行为和有限维约化，相关工作发表在《Applied Mathematics & Optimization》、《Journal of Nonlinear Science》。
活动内容摘要：
In this lecture, we consider the finite-dimensional reduction of the asymptotic dynamics of one-dimensional nonlocal Kirchhoff-type parabolic equations, where the diffusion coefficient depends on the $L^2$-norm of the gradient of the solution. Specifically, we establish the existence (without uniqueness) of an $\varepsilon$-regular mild solution and a global attractor for initial data in $L^2$. Importantly, by employing a time transformation (one for each solution) that converts the nonlocal term into a nonlinear term, we construct an inertial manifold for initial data in $H_0^1$, which implies that the global attractor is the graph of a Lipschitz function over a finite-dimensional subspace of the phase space, thereby revealing that the long-time behavior of this infinite-dimensional system can be completely described by a finite-dimensional system of ordinary differential equations.
主持人：孙春友