2021年2月25日
Stability for stationary solutions of a nonlocal Allen-Cahn equation
Journal of Differential Equations
- ,
- ,
- ,
- 巻
- 275
- 号
- 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
- ID情報
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- DOI : 10.1016/j.jde.2020.11.024
- ISSN : 0022-0396
- eISSN : 1090-2732
- SCOPUS ID : 85096476624