CONTENTS -- Preface -- Well-Posedness for a Ginzburg-Landau Model in Superfluidity V. Berti, M. Fabrizio -- 1 Introduction -- 2 A Ginzburg-Landau model for superfluidity -- 2.1 Thermodynamical consistence of the model -- 2.2 Rotation of a superfluid -- 3 Well-posedness of the problem -- References -- Spherical Tolman-Bondi Models in Cosmology 1. Bochicchio, E. Laserra -- 1 Introduction -- 2 The principal curvatures in spherical symmetry and solutions of evolution equations -- 3 Qualitative evolution of a relativistic r-shell -- References -- Nonlinear Stability of a SIRS Epidemic Model with Convex Incidence Rate B. Buonomo, S. Rionero -- 1 Introduction -- 2 Equilibria -- 3 Nonlinear stability/instability -- 4 Global nonlinear asymptotic stability -- 5 Conclusions -- Acknowledgements -- References -- On the Dynamics of a Binary Model for the Competition between Bacteria and Innate Immune System M. Cerasuolo, P. Fergola, S. Rionero -- 1 Introduction -- 2 Preliminaries -- 3 The associated kinetic system -- 4 Linear Stability and Instability results for the diffusion problem (1)-(2) -- Acknowledgement -- References -- Spatial Evolution in Linear Thermoelasticity S. Chirita, M. Ciarletta -- 1 Introduction -- 2 Formulation of problem -- 3 Spatial evolution in the low frequency range -- 4 A semi-infinite cylinder -- 5 Some comments -- Acknowledgement -- References -- On the Nonautonomous Lotka-Volterra System R. De Luca, S. Rionero -- 1 Introduction -- 2 Stability of (x, y) through model (3) -- 3 Stability of (x, y) through model (4) -- References -- Structure Order Balance Law and Phase Transitions M. Fabrizio -- 1 Introduction -- 2 Balance law on the structure order -- 3 First order phase transition -- 4 Water-vapor phase transition -- References -- Sui Problemi al Contorno Mobile J.N. Flavin -- Diffusione Unidimensionale con un Contorno Mobile.

Delle Osservazioni -- References -- A Phase-Field Model for Liquid-Vapor Transitions Induced by Temperature and Pressure A. Berti, C. Giorgi -- 1 Introduction -- 1.1 The phase diagram -- 1.2 The energy-temperature and Andrews density-pressure diagrams -- 2 Thermodynamics and phase-field equations -- 3 Free energy density -- 4 The vapor pressure curve -- References -- Wave Propagation in Continuously-Layered Media G. Caviglia, A. Morro -- 1 Introduction -- 2 Waves in stratified media -- 3 Variational formulation -- 3.1 Fundamental solutions -- 3.2 Existence and uniqueness -- 4 A basis of solutions -- 4.1 Successive approximations -- 5 Reflection-transmission problem -- 6 Conclusions -- Acknowledgement -- References -- Nonlinear Stability for Reaction-Diffusion Models G. Mulone -- 1 Introduction -- 2 Linear and nonlinear stability by the reduction method -- 3 Applications and global stability results -- 3.1 A 2-dimensional competition model -- 3.2 The asymmetric May-Leonard model with diffusion -- 3.3 An epidemic model with diffusion -- 4 Conclusion -- References -- On the Spatial Behaviour for Transversely Isotropic Plates F. Passarella, V. Zampoli -- 1 Introduction -- 2 Basic model -- 3 Spatial behaviour of transient solutions -- References -- Liapunov Functionals for the Coincidence between the First and the Second Liapunov Stability Methods S. Rionero -- 1 Introduction -- 2 Methodology for obtaining Liapunov functions linked to the A invariants -- 3 The case n = 3 -- 4 Another Liapunov functional for the case n = 3 -- 5 Final Remarks -- Acknowledgements -- References -- A Classical Approach of a Multi-Temperature Mixture of Fluids T. Ruggeri -- 1 Mixtures in rational thermodynamics -- 2 A Variant of Classical approach for multi-temperature mixture -- 3 Entropy principle and constitutive equations -- 4 Conclusion -- Acknowledgment -- References.

On the Displacement Problem of Plane Linear Elastostatics R. Russo -- 1 Introduction -- 2 The elastic simple layer potential -- 3 Existence and uniqueness theorems -- References -- Modelling of Capillary Forces in Viscous Fluids of Grade Two A. Sellitto, V. Triani, V.A. Cimmelli -- 1 Introd uction -- 2 Outline of the extended Liu procedure -- 3 Restrictions placed by second law -- 4 Conclusions -- Acknowledgements -- References -- Absorbing Sets of the Positive Solutions of the Schnackenberg Reaction-Diffusion System under Neumann Homogeneous Boundary Conditions S. Rionero, A. Tataranni -- 1 Introduction -- 2 Preliminaries -- 3 Absorbing sets -- Acknowledgements -- References -- On the Deformation of the Surface of an Elastic Medium with a Cavity V. Tibullo, V. Zampoli -- 1 Introduction -- 2 Problem formulation -- 3 Solution of the problem -- 4 Green's function for the Laplace equation in the half-plane -- 5 Reduction to an integral equation -- 6 Numerical examples -- 7 Conclusions -- References -- Exploitation of Second Law for Second Grade Fluids: Generalized Coleman-Noll and Liu Procedures in Comparison V. Triani, A. Sellitto, V.A. Cimmelli -- 1 Introduction -- 2 An extended Coleman-Noll procedure -- 3 Equivalence with the extended Liu procedure -- 4 Conclusions -- Acknowledgements -- References -- Longtime Behaviour of the Solutions of a Nonlinear Parabolic Reaction-Diffusion Equation under Robin Boundary Data S. Rionero, M. Vitiello -- 1 Introduction -- 2 Statement of the problem -- 3 Existence result -- 4 Global attractor -- 5 Blow Up -- Acknowledgements -- References.