論文

査読有り
2021年2月25日

Stability for stationary solutions of a nonlocal Allen-Cahn equation

Journal of Differential Equations
  • Yasuhito Miyamoto
  • ,
  • Tatsuki Mori
  • ,
  • Tohru Tsujikawa
  • ,
  • Shoji Yotsutani

275
開始ページ
581
終了ページ
597
記述言語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.jde.2020.11.024

© 2020 Elsevier Inc. We consider the dynamics of a nonlocal Allen-Cahn equation with Neumann boundary conditions on an interval. Our previous papers [2,3] obtained the global bifurcation diagram of stationary solutions, which includes the secondary bifurcation from the odd symmetric solution due to the symmetric breaking effect. This paper derives the stability/instability of all symmetric solutions and instability of a part of asymmetric solutions. To do so, we use the exact representation of symmetric solutions and show the distribution of eigenvalues of the linearized eigenvalue problem around these solutions. And we show the instability of asymmetric solutions by the SLEP method. Finally, our results with respect to stability are supported by some numerical simulations.

リンク情報
DOI
https://doi.org/10.1016/j.jde.2020.11.024
Scopus
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85096476624&origin=inward
Scopus Citedby
https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85096476624&origin=inward
ID情報
  • DOI : 10.1016/j.jde.2020.11.024
  • ISSN : 0022-0396
  • eISSN : 1090-2732
  • SCOPUS ID : 85096476624

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