Trends in Applications of Mathematics to MechanicsElisabetta Rocca, Ulisse Stefanelli, Lev Truskinovsky, Augusto Visintin 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. |
Contents
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Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures | 23 |
What Does RankOne Convexity Have to Do with Viscosity Solutions? | 52 |
On Friedrichs Inequality Helmholtz Decomposition Vector Potentials and the divcurl Lemma | 65 |
Variational Analysis of Nematic Shells | 81 |
Modeling of Microstructures in a Cosserat Continuum Using Relaxed Energies | 103 |
From Nonlinear to Linear Elasticity in a Coupled RateDependentIndependent System for Brittle Delamination | 126 |
Three Examples Concerning the Interaction of Dry Friction and Oscillations | 159 |
Numerical Approach to a Model for Quasistatic Damage with Spatial BVRegularization | 178 |
A Prototypical Example | 205 |
Limiting Problems for a Nonstandard Viscous CahnHilliard System with Dynamic Boundary Conditions | 217 |
On a CahnHilliardDarcy System for Tumour Growth with Solution Dependent Source Terms | 243 |
Molecular Extended Thermodynamics of a Rarefied Polyatomic Gas | 265 |
A Comparison of Two Settings for Stochastic Integration with Respect to Lévy Processes in Infinite Dimensions | 288 |
Other editions - View all
Trends in Applications of Mathematics to Mechanics Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin No preview available - 2018 |
Trends in Applications of Mathematics to Mechanics Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin No preview available - 2018 |
Common terms and phrases
Anal bounded Cahn–Hilliard compound Poisson process constant continuous continuum convergence covariance operator curl damage decomposition defined Definition denote density discrete domain dynamic boundary conditions elastic energetic solutions equation exists finite function gradient Helmholtz decomposition hmin inequality integration with respect Itô formula jump measure Lemma Lévy measure Lévy process limit linear Lipschitz domains lower semicontinuity martingale material Math Mathematics Mech microstructures minimization nonlinear numerical obtain optimal Peszat and Zabczyk phase Poisson random measure polyatomic problem proof properties Proposition quadratic variation quasiconvex rank-one convex rate-independent relaxed right-hand side Ruggeri satisfies Sect semistable energetic sequence ſº space of integrands Springer square-integrable square-integrable Lévy martingale stochastic integration Theorem theory U-valued variable vector field Wiener process Young measures