报告题目：Algorithm and numerical simulation for direct and inverse problem of the parabolic equation with time-dependent boundaries

报告摘要：In this talk we discuss problems of a class of non-classical parabolic equations in which the boundaries are time-dependent function, which arise from Ductal Carcinoma In Situ(DCIS). In the direct problem part, on using the several transformation and heat potential theory, we established the integral form of solution and proved the existence and uniqueness of solution. Then we consider the inverse problem of determining the potential function of model from incisional biopsy information in the view of DCIS. Algorithm and numerical simulation for both problems are included to demonstrate the validity and applicability of solutions.

报告人：Yongzhi Xu，Professor（University of Louisville, USA）

时 间：5月20日（周三）下午15：00—16：15

地 点：图书馆五楼学术讨论空间（二）

人物名片：

Yongzhi Xu is a full professor of Mathematics at University of Louisville. He received his B.S. and M.S. in applied mathematics from SunYat-SenUniversity and PhD in applied mathematics from University of Minnesota. He joined the University of Louisville in 2004. His major research areas are partial differential equations, its computation and applications involved inverse scattering problems, mathematical modeling of breast cancer computational acoustics, function theoretic methods for partial differential equations, elastic and thermoelastic problems, biomathematics and medical imaging problems. He has published more than 100 peer reviewed papers, served as the Chief Editor of Applicable Analysis and the Chief Editor of Complex Variables and Elliptic Equations. He is the vice president of International Society for Analysis, its Applications and Computation (ISAAC).