报告题目：A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonlinear elliptic PDEs/systems by Legendre-Gauss-lobatto pseudospectral method

报告人： 李昭祥 教授（上海师范大学）

报告时间：2022年8月19日（星期五） 9:30-10:30

报告地点：腾讯会议：546-453-674

校内联系人：张旭平 副教授  联系电话：84708351-8025

报告摘要：In this talk, in order to find more solutions to nonlinear elliptic systems, a new augmented singular transform (AST) is developed to form a barrier surrounding previously found solutions so that an algorithm search from outside cannot pass the barrier and penetrate into the inside to reach a previously found solution. Thus a solution found by the algorithm must be new. Mathematical justifications of AST formulation are established. A partial Newton-correction method is designed accordingly to solve the augmented problem and to satisfy a constraint in AST. The new method is applied to numerically investigate multiple solutions to nonlinear elliptic systems by Legendre-Gauss-lobatto pseudospectral method.

报告人简介：李昭祥，教授，计算数学专业博士研究生导师.2008年6月于上海师范大学计算数学专业获得博士学位. 2013年2月-2014年2月赴美国德克萨斯州A&M大学数学系访学. 目前主持国家自然科学基金面上项目和上海市自然科学基金面上项目各1项，主持完成上海市自然科学基金面上项目、国家博士后基金面上项目、上海市教委创新项目和优秀青年教师项目各1项，参与多项国家和省部级项目；主持上海市教委重点课程2项；在《J. Comput. Phys.》、《J. Sci. Comput.》、《Comm. Comput. Phys.》和《Sci. China Math.》等国内外学术期刊上发表学术论文30余篇.