ID | 57815 |
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Author |
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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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.
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Keywords | Allen–Cahn equation
stationary solution
comparison theorem
discretized
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Note | Mathematics Subject Classification. Primary 34A33; Secondary 35K57.
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Published Date | 2020-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume62
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 197
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End Page | 210
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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Copyright Holders | Copyright©2020 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol62/iss1/5
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