报告题目：Global well-posedness ,exponential stability for Maxwell equations under delayed boundary conditions in metamaterials and its finite element methods
报告人：姚昌辉
报告摘要：In,this report, We first develop an initial-boundary value problem derived from the Maxwell's system with a nonlinear feedback-type boundary mechanism in metamaterials, which both involves polarization,magnetization effect and time-localized delay effect in a bounded domain. Based on the nonlinear semigroup theory and the properties of viscoelasticity theory, we show the well-posedness of solution in an appropriate Hilbert space. Under some suitable assumptions and geometric conditions, we prove the exponential stability of the Maxwell's system. Then, we combine finite element method with second-order central difference scheme, and construct a full discrete scheme and present the result of stability. By virtue of the projection operator, the discretization of convolution terms and the properties of the nonlinear terms, we show the error estimate with convergent rate $O(\tau^2 + h^{s})$. At last, numerical examples confirm the theoretical results. Especially, when the nonlinear delay term is controlled by the nonlinear instantaneous term($\gamma_1c_1<\gamma_2c_2$), the propagation of numerical solution demonstrates the notable stability.
报告人简介：姚昌辉，男，博士，河南省特聘教授，郑州大学博士生导师。中国数学会计算数学分会常务理事，中国仿真学会不确定性系统分析与仿真专业委员会常务委员，河南省数字图形图像学会主任委员。2006年6月在中国科学院获得计算数学专业理学博士学位， 2008在挪威Bergen大学获得应用数学专业哲学博士学位。 曾主持国家自然科学基金青年基金1项，国家自然科学基金面上项目2项，参与完成国家自然科学基金面上项目2项，2021年出版河南省“十四五”普通高等教育规划教材《数值分析》，2022年获得由河南省人民政府颁发的自然科学奖二等奖。
时间：2024年6月3日16:00
地点：教科楼B座863
邀请人：任金城
主办单位：数学与信息科学学院
