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Variational and PDE methods in nonli...

Bethuel, Fabrice.

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Variational and PDE methods in nonlinear science = Cetraro, Italy 2023 /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Variational and PDE methods in nonlinear science/ by Fabrice Bethuel ... [et al.].
Reminder of title:	Cetraro, Italy 2023 /
other author:	Bethuel, Fabrice.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	ix, 190 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	- 1. Scalar and Vectorial Allen-Cahn Equations and their Asymptotics -- 2. Microstructures in the Modelling of Shape-Memory Alloys: Rigidity, Flexibility and Scaling -- 3. Singular Minimizers in Nonlinear Elasticity.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial. -
Online resource:	https://doi.org/10.1007/978-3-031-87202-0
ISBN:	9783031872020

Variational and PDE methods in nonlinear science = Cetraro, Italy 2023 /
Variational and PDE methods in nonlinear scienceCetraro, Italy 2023 /[electronic resource] :by Fabrice Bethuel ... [et al.]. - Cham :Springer Nature Switzerland :2025. - ix, 190 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,v. 23662946-1820 ;. - Lecture notes in mathematics ;v. 2366..

- 1. Scalar and Vectorial Allen-Cahn Equations and their Asymptotics -- 2. Microstructures in the Modelling of Shape-Memory Alloys: Rigidity, Flexibility and Scaling -- 3. Singular Minimizers in Nonlinear Elasticity.

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.

ISBN: 9783031872020

Standard No.: 10.1007/978-3-031-87202-0doiSubjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Variational and PDE methods in nonlinear science = Cetraro, Italy 2023 /
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520 $a 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.
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