Variational and PDE Methods in Nonlinear Science

Fabrice Bethuel

ISBN 10: 3031872010 / ISBN 13: 9783031872013

Published by Springer, Berlin, Springer Nature Switzerland, European Mathematical Society, Università Degli Studi Di Napoli Federico II, Istituto Nazionale Di Alta Matematica Francesco Severi, Gruppo Nazionale Per L'analisi Matematica, La Probabilità E Le Loro Applicazioni, Università Degli Studi Di Verona, Springer, 2025

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -This bookpresents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school Variational and PDE Methods in Nonlinear Science , held in Cetraro (Italy), July 10 14, 2023.Fabrice Bethuel discusses aympototics for Allen Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers. The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory. 189 pp. Englisch.

Seller Inventory # 9783031872013

Bibliographic Details

• Title: Variational and PDE Methods in Nonlinear Science
• Publisher: Springer, Berlin, Springer Nature Switzerland, European Mathematical Society, Università Degli Studi Di Napoli Federico II, Istituto Nazionale Di Alta Matematica Francesco Severi, Gruppo Nazionale Per L'analisi Matematica, La Probabilità E Le Loro Applicazioni, Università Degli Studi Di Verona, Springer
• Publication Date: 2025
• Language: English
• ISBN 10: 3031872010
• ISBN 13: 9783031872013
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 11D millimeters 235 millimeters width by 155 millimeters height by 11 millimeters depth
• Weight: 312 grams

About this title

Synopsis

This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school “Variational and PDE Methods in Nonlinear Science”, held in Cetraro (Italy), July 10–14, 2023.

Fabrice Bethuel discusses aympototics for Allen–Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers.   

The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory.