题目：Global bifurcation structure of steady-states for a nonlocal Allen-Cahn equation in dimension one

报告人: Prof. Kousuke Kuto（University of Electro Communications, Japan）    

Abstract: This talk is concerned with the Neumann problem of the 1D stationary Allen-Cahn equation with a nonlocal term. Since this nonlocal term is given as the average of the unknown function, every odd-symmetric solution counteracts the nonlocal effect, and thereby, becomes a stationary solution of the Allen-Cahn equation without nonlocal term. Namely, the set of odd-symmetric solutions of the nonlocal problem forms a bifurcation branch of the Chafee-Intante problem which emanates from a pitchfork bifurcation point on the branch of the trivial solution. A main result reveals that the nonlocal term induces a symmetry breaking bifurcation point on the branch of odd-symmetric solutions. This talk also mentions the global behavior of the bifurcation branch of asymmetric solutions.
This talk is based on a joint work with Tatsuki Mori (Osaka Univ.),Tohru Tsujikawa (Univ. of Miyazaki) and Shoji Yotsutani (Ryukoku Univ.).

时间：2018年3月23日（周五） 10:30-11:30

地点：首都师大新教二楼 827教室

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