Axially symmetric solutions of Allen-Cahn equation with finite Morse index

2019/01/31 by Changfeng Gui, Kelei Wang, Gui, Changfeng +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1901.11263

openalex publication_date 2019/01/31 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

In this paper we study axially symmetric solutions of Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between 4 and 10. In dimension 3, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals 1.

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