کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4604261 | 1337428 | 2014 | 44 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Unilateral gradient flow of the Ambrosio–Tortorelli functional by minimizing movements
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Motivated by models of fracture mechanics, this paper is devoted to the analysis of a unilateral gradient flow of the Ambrosio–Tortorelli functional, where unilaterality comes from an irreversibility constraint on the fracture density. Solutions of such evolution are constructed by means of an implicit Euler scheme. An asymptotic analysis in the Mumford–Shah regime is then carried out. It shows the convergence towards a generalized heat equation outside a time increasing crack set. In the spirit of gradient flows in metric spaces, a notion of curve of maximal unilateral slope is also investigated, and analogies with the unilateral slope of the Mumford–Shah functional are also discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 31, Issue 4, July–August 2014, Pages 779–822
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 31, Issue 4, July–August 2014, Pages 779–822
نویسندگان
Jean-François Babadjian, Vincent Millot,