报告人：A. S. Hendy（乌拉尔联邦大学）

报告题目：Identification of an unknown spatial source function in a multidimensional hyperbolic partial differential equation with interior degeneracy

报告摘要：A reconstruction of an unknown source function is considered for hyperbolic partial differential equations with interior degeneracy. We identify the spatial element of the source term of a degenerate wave equation using the final observation data. The existence and uniqueness of the direct problem with interior degeneracy within the spatial domain are stated and proved. The inverse problem can be formulated as a nonlinear optimization problem and the unknown source term can be characterized as the solution to a minimization problem. The Tikhonov regularization technique is employed to accomplish the inclusion of noise in the input data, based on the insertion of the regularization term into the cost functional. The conjugate gradient algorithm in conjunction with Morozov's discrepancy principle as a stopping criterion is then utilized to develop an iterative reconstruction procedure. Finally, some numerical simulation results are provided to show the performance of the proposed scheme in one and two dimensions.

报告时间：2024年11月7日（星期四）10:00-12:00

报告地点：科技楼南706室

邀请人：李东方

报告人简介：A. S. Hendy，俄罗斯乌拉尔联邦大学研究员，主要从事非局部微分方程、抛物方程和反问题方面的高效数值算法和理论的研究。他目前担任Math.Comput.Simu.等杂志的编委，在计算数学知名期刊发表论文90余篇。