Trends in Applications of Mathematics to Mechanics

Description

This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5–9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics. Front Matter ....Pages i-ix Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints (Elisa Davoli, Irene Fonseca)....Pages 1-21 Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures (Agnieszka Kałamajska, Stefan Krömer, Martin Kružík)....Pages 23-51 What Does Rank-One Convexity Have to Do with Viscosity Solutions? (Pablo Pedregal)....Pages 53-64 On Friedrichs Inequality, Helmholtz Decomposition, Vector Potentials, and the div-curl Lemma (Ben Schweizer)....Pages 65-79 Variational Analysis of Nematic Shells (Giacomo Canevari, Antonio Segatti)....Pages 81-102 Modeling of Microstructures in a Cosserat Continuum Using Relaxed Energies (Muhammad Sabeel Khan, Klaus Hackl)....Pages 103-125 From Nonlinear to Linear Elasticity in a Coupled Rate-Dependent/Independent System for Brittle Delamination (Riccarda Rossi, Marita Thomas)....Pages 127-157 Three Examples Concerning the Interaction of Dry Friction and Oscillations (Alexander Mielke)....Pages 159-177 Numerical Approach to a Model for Quasistatic Damage with Spatial BV -Regularization (Sören Bartels, Marijo Milicevic, Marita Thomas)....Pages 179-203 Rigidity Effects for Antiferromagnetic Thin Films: A Prototypical Example (Andrea Braides)....Pages 205-216 Limiting Problems for a Nonstandard Viscous Cahn–Hilliard System with Dynamic Boundary Conditions (Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels)....Pages 217-242 On a Cahn–Hilliard–Darcy System for Tumour Growth with Solution Dependent Source Terms (Harald Garcke, Kei Fong Lam)....Pages 243-264 Molecular Extended Thermodynamics of a Rarefied Polyatomic Gas (Tommaso Ruggeri)....Pages 265-287 A Comparison of Two Settings for Stochastic Integration with Respect to Lévy Processes in Infinite Dimensions (Justin Cyr, Sisi Tang, Roger Temam)....Pages 289-373