Lewicka Calculus of Variations on Thin Prestressed Films 9783031174940

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Автор: Lewicka
Название: Calculus of Variations on Thin Prestressed Films
ISBN: 9783031174940
Издательство: Springer
Классификация:

Дифференциальное исчисление и дифференциальные уравнения

Дифференциальная и риманова геометрия

Оптимизация

Материаловедение

ISBN-10: 3031174941
Обложка/Формат: Hardback
Страницы: 448
Вес: 0.85 кг.
Дата издания: 02.05.2023
Серия: Progress in Nonlinear Differential Equations and Their Applications
Язык: English
Издание: 1st ed. 2023
Иллюстрации: 15 tables, color; 16 illustrations, color; 4 illustrations, black and white; ix, 448 p. 20 illus., 16 illus. in color.
Размер: 235 x 155
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: Asymptotic methods in elasticity
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria. It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry – that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations – that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate. Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers. While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book. The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.
Дополнительное описание: Introduction.- Part I: Tools in Mathematical Analysis.- ?-Convergence.- Korn's Inequality.- Friesecke-James-M?ller’s Inequality.- Part II: Dimension Reduction in Classical Elasticity.- Limiting Theories for Elastic Plates and Shells: Nonlinear Bending.- L

Calculus of Variations on Thin Prestressed Films, Lewicka