报告题目：Simultancous determination of the order and a coeffcient in a fractional diffusion-wave equation

报 告 人：魏婷教授（兰州大学）

报告时间：2024年4月17日  16:00-17:00

报告地点：格物楼528

报告摘要：

This paper recovers the order of fractional derivative and a time-dependent potential coefficient in a time-fractional diffusion wave equation by an integral condition or one point measurement on the boundary. The Lipschitz continuity of the forward operators from the unknown order and coefficient to the given data are achieved in terms of the integral equation held by the solution of the direct problem. We also obtain the uniqueness for the considered inverse problems in terms of somewhat general conditions to the given functions. Moreover, we propose a Tikhonov-type regularization method and prove the existence of the regularized solution and its convergenee to the exact solution under a suitable regularization parameter choice. Then we use a linearized iteration algorithm to recover numerically the order and time-dependent potential coeficient simultaneously. Two numerical examples for one- and two-dimensional cases are provided to display the eficient of the proposed method.

报告人简介：

魏婷，教授，博导。入选2006年度的教育部新世纪优秀人才支持计划。主要研究方向是数学物理方程反问题的计算方法及理论研究，目前主要从事分数阶扩散及扩散波方程反问题的理论与计算方法研究。已主持完成4项国家自然科学基金面上项目，目前正在主持1项面上项目“反常扩散中多参数同时辨识问题的唯一性理论及算法研究”，在Inverse Probl., SIAM J. Numer. Anal., Adv. Comput. Math.等学术刊物上发表学术论文100余篇，被SCI收录论文103篇，在Web of Science数据库中他引2600余次。曾多次赴香港、日本、美国作访问学者，并参加了在日本、澳大利亚、中国、斯洛伐克、韩国、芬兰、美国、德国巴西、新加坡、俄罗斯等国家及香港、台湾地区举行的国际会议。