Mathematical Journal of Okayama University volume62 issue1
Amy Poh Ai Ling
Division of Mathematics and Physics, Graduate School of Natural Science and Technology, Okayama University
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.
Mathematics Subject Classification. Primary 34A33; Secondary 35K57.