主講人介紹：Biographical Sketches---Dr. Jianxin Zhou（周建新） (Email:[email protected], Webpage:www.math.tamu.edu/~jzhou) Education Background: Pennsylvania State University, University Park, PA, USA, Optimal Control, Postdoc, 1987. Pennsylvania State University, University Park, PA, USA, Mathematics, Ph. D., 1986. Shanghai University of Science & Tech., Shanghai, China, Applied Mathematics, M.S., 1982. Shanghai University of Science & Tech., Shanghai, China, Computational Mathematics, 1977. Professional Working Experience. 6/2015-5/2016: Oversea Distinguished Professor, Hunan Normal University, China 5/2004-6/2004: Feng Kang Professor, Shanghai University, Shanghai, China 1999-present: Full Professor, Texas A&M University, College Station, TX, USA 1993-1999: Associate Professor, Texas A&M University, College Station, TX. USA 1987-1993: Assistant Professor, Texas A&M University, College Station, TX. USA Research Interests: Applied Analysis and Scientific Computation in differential multiple solution problems, multi-level optimization, control and games theory. Research Grants: supported by NSF and other funding agencies. Publications (published more than 80 papers and 5 advanced books) Most significant contribution to mathematics: Pioneer work on developing computational theory and methods for finding multiple (unstable) solutions in various differential systems. His results have been used in books, in research and graduate education by other researchers around the world and have established him as a respected international leader in this research area. Five Most Closely Related Publications: 1. A minimax method for finding multiple critical points and its applications to semilinear PDE, SIAM J. Sci. Comp., 23(2001) 840-865. (with Y. Li) 2. A local min-orthogonal method for finding multiple saddle points, JMAA, 291(2004) 66-81.
內容介紹：In this talk, in order to find more solutions to a nonvariational quasilinear PDE, 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 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 bifurcation, symmetry-breaking phenomena to a nonvariational quasilinear elliptic equation through finding multiple solutions.