Mathematical Models and Methods for Smart Materials : Cortona, Italy, 25-29 June 2001

by Indam Meeting Mathematical Models for Smart Material; Fabrizio, Mauro; Lazzari, Barbara; Morro, Angelo; Fabrizio, Mauro; Istituto Nazionale Di Alta Matematica (Italy)

• ISBN13: 9789812382351
• ISBN10: 9812382356
• Format: Hardcover
• Copyright: 2002-12-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

This book contains the papers presented at the conference on "Mathematical Models and Methods for Smart Materials, " held in Italy in 2001. The papers are divided into four parts: "Methods in Materials Science" deals mainly with mathematical techniques fo the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems. "Modelling of Smart Materials" is devoted to models of superfluids, superconductors, materials with memory, nonlinear elastic solids, and damaged materials. In the elaboration of the models, thermodynamic aspects play a central role in the characterization of the constitutive properties. "Well-Posedness in Materials with Memory" deals with existence, uniqueness and stability for the solution of problems, most often expressed by integrodifferential equations, which involve materials with fading memory. Also, attention is given to exponential decay in viscoelasticity, inverse problems in heat conduction with memory, and automatic control for parabolic equations. "Analytic Problems in Phase Transitions" discusses nonlinear partial differential equations associated with phase transitions, and hysteresis, possibly involving fading memory effects. Particular applications are developed for the phase-field model with memory, the Stefan problem with a Cattaneo type equation, the hysteresis in thermo-visco plasticity, and the solid-solid phase transition. Contents: Automatic Control Problems for Integrodifferential Parabolic Equations (C Cavaterra);Phase Relaxation Problems with Memory and Their Optimal Control (P Colli); Unified Dynamics of Particles and Photons (G Ferrarese); Solid-Solid Phase Transition in a Mechanical System (G Gilardi); KAM Methods for Nonautonomous

Table of Contents

Preface
Obituary
Temperance for order/disorder transition in nematics	p. 1
Null Lagrangians and surface interaction potentials in nonlinear elasticity	p. 9
Automatic control problems for integrodifferential parabolic equations	p. 19
Asymptotic partition in the linear thermoelasticity backward in time	p. 31
Internal parameters and superconductive phase in metals	p. 43
Phase relaxation problems with memory and their optimal control	p. 51
Some inverse problems related to the heat equation with memory in non-smooth spatial domains	p. 61
On the minimal free energy and the Saint-Venant principle in linear viscoelasticity	p. 73
Gentili's norm on the process and state spaces in linear viscoelasticity	p. 89
Unified dynamics of particles and photons	p. 103
The problem of the rate of thermalization, and the relations between classical and quantum mechanics	p. 111
Solid-solid phase transition in a mechanical system	p. 123
The minimum free energy of compressible viscoelastic fluids	p. 131
KAM methods for nonautonomous Schrodinger operators	p. 145
Phase-field systems with memory effects in the order parameter dynamics	p. 155
Elliptic problems depending on a parameter in plane curvilinear polygons	p. 165
Fractional diffusion and wave equations	p. 171
Exponential decay on the mean in linear viscoelasticity	p. 189
Recovering a memory kernel in an integrodifferential Stefan problem	p. 197
The fundamental solutions of the time-fractional diffusion equation	p. 207
Some results of pointwise stability for solutions to the Navier-Stokes system	p. 225
Asymptotic behavior for a model of transverse vibration of a bar with linear memory	p. 231
Balance equations in two-fluid models in helium II	p. 235
Thermoelastic plate with thermal interior control	p. 247
A non-stationary model in superconductivity	p. 251
Counterexample to the exponential decay for systems with memory	p. 265
Convergence to the Stefan problem of the hyperbolic phase relaxation problem and error estimates	p. 273
On a thermodynamical model for type-II high-T[subscript c] superconductors. Theory and applications	p. 283
Decay of the energy to partially viscoelastic materials	p. 297
Some remarks on the conserved Penrose-Fife phase field model with memory effects	p. 313
Local solution to Fremond's full model for irreversible phase transitions	p. 323
A scalar model of viscoelasticity with singular memory	p. 329
An existence result for semilinear equations in viscoelasticity: The case of regular kernels	p. 343
Phase transitions and hysteresis in one-dimensional thermo-plasticity	p. 355
Longterm dynamics of a conserved phase-field system with memory	p. 363
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