Mathematical Journal of Okayama University 62巻 1号
2020-01 発行

Existence and stability of stationary solutions to the Allen-Cahn equation discretized in space and time

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 Kaken ID publons researchmap
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.