Series On Advances In Mathematics For Applied Sciences: Mathematical Models And Methods For Smart Materials (PDF)

This book contains the papers presented at the conference on âMathematical Models and Methods for Smart Materialsâ, held in Italy in 2001. The papers are divided into four parts:âMethods in Materials Scienceâ deals mainly with mathematical techniques for 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.âModelling of Smart Materialsâ 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.âWell-Posedness in Materials with Memoryâ 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.âAnalytic Problems in Phase Transitionsâ 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.