Mathematical Journal of Okayama University volume62 issue1

2020-01 発行

Amy Poh Ai Ling
Division of Mathematics and Physics, Graduate School of Natural Science and Technology, Okayama University

Taniguchi, Masaharu
Research Institute for Interdisciplinary Science, Okayama University
ORCID
Kakenhi
publons

Publication Date

2020-01

Abstract

The existence and stability of the Allen–Cahn equation discretized in space and time are studied in a finite spatial interval. If a parameter is less than or equals to a critical value, the zero solution is the only stationary solution. If the parameter is larger than the critical value, one has a positive stationary solution and this positive stationary solution is asymptotically stable.

Keywords

Allen–Cahn equation

stationary solution

comparison theorem

discretized

Comments

Mathematics Subject Classification. Primary 34A33; Secondary 35K57.