报告题目 (Title)：A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonlinear elliptic PDEs/systems (增广奇异变换以及求解非线性椭圆偏微分方程的偏牛顿-校正法)

报告人 (Speaker)：李昭祥 教授（上海师范大学）

报告时间 (Time)：2022年9月3日(周六) 15:00-16:00

报告地点 (Place)：腾讯会议 （会议 ID：464 499 443）

邀请人(Inviter)：蔡敏

主办部门：理学院数学系

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.