000			02926i0n a2200385 4500
001			u7431
003			SIRSI
005			20251112200007.0
008			|a250702s2025 sz | r |||0 eng d
020			_a9783031872013
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ _dclrauoh _erda
100			_aBethuel, Fabrice., _eauthor.
245	1	0	_aVariational and PDE Methods in Nonlinear Science : _bCetraro, Italy 2023 / _cby Fabrice Bethuel, Duvan Henao, Angkana Rüland ; edited by Fabrice Bethuel, Giandomenico Orlandi, Bianca Stroffolini.
250			_aFirst edition: 2025.
264			_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2025.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
500			_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			_aThis 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			_aMathematical optimization.
650			_aCalculus of variations.
650			_aGeometry, Differential.
650			_aGlobal analysis (Mathematics).
650			_aManifolds (Mathematics).
650			_aFluid mechanics.
650			_aCalculus of Variations and Optimization.
650			_aDifferential Geometry.
650			_aGlobal Analysis and Analysis on Manifolds.
650			_aEngineering Fluid Dynamics.
700			_aHenao, Duvan.
700			_aRüland, Angkana.
700			_aOrlandi, Giandomenico.
700			_aStroffolini, Bianca.
999			_c6447 _d6447