國立虎尾科技大學 |

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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Variational and PDE methods in nonlinear science/ by Fabrice Bethuel ... [et al.].
其他題名:	Cetraro, Italy 2023 /
其他作者:	Bethuel, Fabrice.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	ix, 190 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Engineering Fluid Dynamics. -
電子資源:	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 ;1943..

- 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:

670525
Engineering Fluid Dynamics.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Variational and PDE methods in nonlinear science = Cetraro, Italy 2023 /
LDR:02669nam a2200349 a 4500 001 1159708
003 DE-He213
005 20250702130345.0
006 m d
007 cr nn 008maaau
008 251029s2025 sz s 0 eng d
020 $a 9783031872020 $q (electronic bk.)
020 $a 9783031872013 $q (paper)
024 7 $a 10.1007/978-3-031-87202-0 $2 doi
035 $a 978-3-031-87202-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBU $2 bicssc
072 7 $a MAT042000 $2 bisacsh
072 7 $a PBU $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .V299 2025
245 0 0 $a Variational and PDE methods in nonlinear science $h [electronic resource] : $b Cetraro, Italy 2023 / $c by Fabrice Bethuel ... [et al.].
260 $a Cham : $c 2025. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a ix, 190 p. : $b ill. (some col.), digital ; $c 24 cm.
338 $a online resource $b cr $2 rdacarrier
490 1 $a Lecture notes in mathematics, $x 2946-1820 ; $v v. 2366
505 0 $a - 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.
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.
650 2 4 $a Engineering Fluid Dynamics. $3 670525
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Differential Geometry. $3 671118
650 1 4 $a Calculus of Variations and Optimization. $3 1366302
650 0 $a Differential equations, Nonlinear. $3 528440
650 0 $a Differential equations, Partial. $3 527784
700 1 $a Bethuel, Fabrice. $3 1201289
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 1943. $3 882220
856 4 0 $u https://doi.org/10.1007/978-3-031-87202-0
950 $a Mathematics and Statistics (SpringerNature-11649)