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
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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.