非线性分析研讨班：Multiple-end solutions of the Allen-Cahn equation on the plane

中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：刘勇（中国科学技术大学）

题  目：Multiple-end solutions of the Allen-Cahn equation on the plane

时  间：2023.10.25（星期三）11:00-11:50

地  点：思源楼S813

摘  要：Allen-Cahn equation is a classical model arising from phase transition and closely related to the minimal surface theory. In dimension two, an important class of solutions to this equation is the so called multiple-end solutions. They have finite Morse index. While there already exist some results on the construction of these solutions near the boundary of the whole moduli space of multiple-end solutions, a general variational construction is still missing. In this talk we prove that there exists a family of 6-end solutions with prescribed slopes using minimax arguments. This is joint work with Jun Wang and Wen Yang.