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A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional.
- Source :
-
Asymptotic Analysis . 2023, Vol. 135 Issue 3/4, p349-362. 14p. - Publication Year :
- 2023
-
Abstract
- This note addresses the question of convergence of critical points of the Ambrosio–Tortorelli functional in the one-dimensional case under pure Dirichlet boundary conditions. An asymptotic analysis argument shows the convergence to two possible limits points: either a globally affine function or a step function with a single jump at the middle point of the space interval, which are both critical points of the one-dimensional Mumford–Shah functional under a Dirichlet boundary condition. As a byproduct, non minimizing critical points of the Ambrosio–Tortorelli functional satisfying the energy convergence assumption as in (Babadjian, Millot and Rodiac (2022)) are proved to exist. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BRITTLE fractures
Subjects
Details
- Language :
- English
- ISSN :
- 09217134
- Volume :
- 135
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Asymptotic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 173759227
- Full Text :
- https://doi.org/10.3233/ASY-231857