Book Description

Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. Contents: Mathematical Models Including a Hysteresis Operator (T Aiki); Modelling Phase Transitions via an Entropy Equation: Long-Time Behavior of the Solutions (E Bonetti); Global Solution to a One Dimensional Phase Transition Model with Strong Dissipation (G Bonfanti & F Luterotti); A Global in Time Result for an Integro-Differential Parabolic Inverse Problem in the Space of Bounded Functions (F Colombo et al.); Weak Solutions for Stefan Problems with Convections (T Fukao); Memory Relaxation of the One-Dimensional CahnOCoHilliard Equation (S Gatti et al.); Mathematical Models for Phase Transition in Materials with Thermal Memory (G Gentili & C Giorgi); Hysteresis in a First Order Hyperbolic Equation (J Kopfovi); Approximation of Inverse Problems Related to Parabolic Integro-Differential Systems of Caginalp Type (A Lorenzi & E Rocca); Gradient Flow Reaction/Diffusion Models in Phase Transitions (J Norbury & C Girardet); New Existence Result for a 3-D Shape Memory Model (I Pawlow & W M Zajaczkowski); Analysis of a 1-D Thermoviscoelastic Model with Temperature-Dependent Viscosity (R Peyroux & U Stefanelli); Global Attractor for the Weak Solutions of a Class of Viscous Cahn-Hilliard Equations (R Rossi); Stability for Phase Field Systems Involving Indefinite Surface Tension Coefficients (K Shirakawa); Geometric Features of p -Laplace Phase Transitions (E Valdinoci). Readership: Applied mathematicians and researchers in analysis and differential equations."