讲座论坛
荔园数学讲坛: Global well-posedness and energy dissipation estimation for Maxwell equations under delayed boundary conditions in metamaterials
发布时间:2022-06-30 08:12:54 2051

内容摘要: 

In this paper, we concentrate on the model of Maxwell’s system in metamaterials with a nonlinear boundary condition, which has considered two partial differential equations of the currents in the free electron related to the polarization and magnetization in metamaterials. Then we attempt to provide a further study for the double convolution of Maxwell’s equations on time domain by Viscoelasticity Theory. Such a new initial boundary value problem is under the assumption of electrical sources and resistance effects are absent. Next the equations are transformed to an abstract nonlinear evolution equation. We proved the existence and uniqueness of solution with respect to the evolution equation by using nonlinear semigroup theory, which mainly explains the existence theory of nonlinear initial boundary value problem through the description of the basic theory of maximal monotone operators in reflexive Banach space. This provides a theoretical foundation for further research. Finally we give the exponential stability of energy with general nonlinear feedbacks on the whole domain.

主讲人简介: 

姚昌辉,男,1977年01月出生,博士、教授、博士生导师。中国仿真学会不确定性系统分析与仿真专业委员会委员,中国数学会计算数学分会理事,河南省智能图像学会理事。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,发表SCI学术论文30多篇,主要侧重于对电磁场问题的数值方法研究。