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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)
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Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
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
Schlagwörter Lyapunov Stability Of Equilibria ; Non-isolated Equilibria ; Obstacle Problem ; Strongly Irreversible Allen-cahn Equation ; Variational Inequality; Evolution; Approximation; Model; Existence; Damage
Sprache englisch
Veröffentlichungsjahr 2024
HGF-Berichtsjahr 2024
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
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
POF Topic(s) 30205 - Bioengineering and Digital Health
Forschungsfeld(er) Enabling and Novel Technologies
PSP-Element(e) G-503800-001
Förderungen Carl Friedrich von Siemens Foundation
Alexander von Humboldt Foundation
JSPS KAKENHI
DOI 10.1017/prm.2024.97
WOS ID 001380747900001
Scopus ID 85212764524
Erfassungsdatum 2025-01-10
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