报告题目：Bayesian inverse method for inverse scattering problems of nonlocal wave equations
报告人：贾骏雄 副教授
报告人单位：西安交通大学
报告时间：2018年4月25日，下午3：00-4:00
报告地点：数学学院九龙湖第一报告厅
报告摘要：
In this talk, we focus on a new wave equation described wave propagation in the attenuation medium. Based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named as fractional Helmholtz equation. According to the physical interpretations, this new model could be divided into two separate models: loss-dominated model and dispersion-dominated model. For the loss-dominated model, well-posedness has been established and the Lipschitz continuity of the scattering field with respect to the scatterer has also been established. Then, we generalize the Bayesian inverse theory in infinite-dimension to allow a part of the noise depends on the target function (the function needs to be estimated). Then, we prove that the estimated function tends to be the true function if both the model reduction error and the white noise vanish. At last, our theory has been applied to the loss-dominated model with absorbing boundary condition.
报告人介绍：
贾骏雄，1987年生，副教授，硕士生导师。2015年在西安交通大学获得理学博士学位，主要研究方向为反演问题的数学理论与算法。主持国家自然科学基金、陕西省自然科学基金、中国博士后基金、中国博士后基金特别资助等科研项目。现已在Inverse Problems、Journal of Differential Equations、Inverse Problems and Imaging、Journal of Scientific Computing、Journal of Functional Analysis等国际刊物发表学术论文18篇，其中第一/通讯作者论文13篇。2017年获得陕西省数学会青年教师优秀论文一等奖、陕西省优秀博士论文奖以及西安交通大学优秀博士论文奖。在第13届国际理论与计算声学、中国数学会年会、第六届分析数学及其应用等国际、国内重要会议上作邀请报告6次。