学术报告-谢资清

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2018-05-14 08:24:00

学术报告

题      目:Solving Singularly Perturbed Neumann Problems for Multiple Solutions

报  告  人:谢资清 教授  (邀请人:李董辉)

                            湖南师范大学


时      间:2018-05-14 09:30--10:30

地      点:学院306

报告人简介:

       湖南师范大学二级教授,理学院院长,湖南省计算数学学会理事长,全国政协委员。


摘      要:

      In this talk, based on the analysis of bifurcation points and Morse indices of trivial solutions at any perturbation value, the generating process of nontrivial positive solutions for a general singularly perturbed Neumann boundary value problem is developed. The bifurcation points of each trivial solution and then the exact critical perturbation value which determines the existence or non-existence of nontrivial positive solutions are verified .An efficient local minimax method based on the bifurcation and Morse theory is
proposed to compute both M-type and W-type saddle points by introducing an adaptive local refinement strategy, a continuation strategy for initial selection and the Newton method to improve the convergence speed. Extensive numerical results are reported to investigate the critical value and present interesting properties of different types of multiple solutions.