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Akagi, G.* ; Efendiyev, M.A.

Lyapunov stability of non-isolated equilibria for strongly irreversible Allen-Cahn equations.

Proc. R. Soc. Edinburgh, Sect. A, DOI: 10.1017/prm.2024.97 (2024)
DOI
Free by publisher: Verlagsversion online verfügbar 01/2026
The present article is concerned with the Lyapunov stability of stationary solutions to the Allen-Cahn equation with a strong irreversibility constraint, which was first intensively studied in [2] and can be reduced to an evolutionary variational inequality of obstacle type. As a feature of the obstacle problem, the set of stationary solutions always includes accumulation points, and hence, it is rather delicate to determine the stability of such non-isolated equilibria. Furthermore, the strongly irreversible Allen-Cahn equation can also be regarded as a (generalized) gradient flow; however, standard techniques for gradient flows such as linearization and Łojasiewicz-Simon gradient inequalities are not available for determining the stability of stationary solutions to the strongly irreversible Allen-Cahn equation due to the non-smooth nature of the obstacle problem.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Lyapunov Stability Of Equilibria ; Non-isolated Equilibria ; Obstacle Problem ; Strongly Irreversible Allen-cahn Equation ; Variational Inequality; Evolution; Approximation; Model; Existence; Damage
ISSN (print) / ISBN 0308-2105
e-ISSN 1473-7124
Zeitschrift Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Verlag Cambridge Univ. Press
Verlagsort Edinburgh Bldg, Shaftesbury Rd, Cb2 8ru Cambridge, England
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
Förderungen Carl Friedrich von Siemens Foundation
Alexander von Humboldt Foundation
JSPS KAKENHI