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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
Open Access Green as soon as Postprint is submitted to ZB.
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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Publication type Article: Journal article
Document type Scientific Article
Keywords 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
Journal Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Publisher Cambridge Univ. Press
Publishing Place Edinburgh Bldg, Shaftesbury Rd, Cb2 8ru Cambridge, England
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)
Grants Carl Friedrich von Siemens Foundation
Alexander von Humboldt Foundation
JSPS KAKENHI