CONTENTS -- Preface -- Conference Data -- On Whitham Equations for Camassa-Holm -- 1. Introduction -- 2. Travelling wave solution for Camassa-Holm -- 3. Whitham equations for Camassa-Holm -- 4. Further perspective -- Acknowledgments -- References -- Inverse Doping Problems for Semiconductor Devices -- 1. Setting of the problem -- 2. Simplified problem and asymptotic analysis -- 3. Steady state inverse doping problem -- 4. Time-dependent inverse doping problem -- References -- Vanishing Viscosity Solutions of Hyperbolic Systems of Conservation Laws with Boundary -- References -- An Operatorial Description of Stock Markets -- 1. Introduction -- 2. The model -- Acknowledgments -- References -- Numerical Simulation of Models for Reacting Polytropic Gases -- 1. Introduction -- 2. The kinetic model -- 3. The hydrodynamic limit -- 4. Numerical simulation of the kinetic equations -- 5. Numerical simulation of the hydrodynamical equations -- 6. Numerical results -- References -- Heat Conduction in a Non-Inertial Frame -- 1. Introduction -- 2. Extended thermodynamics in a non-inertial frame -- 3. Heat conduction between co-axial cylinders -- 4. Solutions -- References -- Nonlinear Stability of Uniform Steady States and Preservation of Sign for a Two-Dimensional Fourth-Order Reaction Diffusion Equation -- 1. Introduction -- 2. Convergence and Positivity of Solutions -- References -- The Non-Relativistic Limit of Relativistic Extended Thermodynamics with Many Moments. Part I: The Balance Equations -- 1. Introduction -- 2. Suggestion from kinetic theory -- 3. A new form for the system (5). -- 4. Appendix -- References -- Hydrodynamic Models for a Two-Band Nonzero-Temperature Quantum Fluid -- 1. Introduction -- 2. Nonzero-temperature hydrodynamic model -- 3. The drift-diffusion model -- Acknowledgements -- References.

Vortex Layers in the Small Viscosity Limit -- 1. Introduction -- 2. The Navier-Stokes equations in a moving curvilinear reference frame -- 3. The vortex layer equations -- 4. Well posedness -- 5. Conclusions -- Appendix -- References -- Mathematical Study of the Small Oscillations of a Pendulum Filled by an Inviscid Incompressible Almost Homogeneous Liquid -- 1. Position of the problem -- 2. Equations of motion -- 3. The case of almost homogeneous liquid -- 4. Operatorial equations of the problem and properties of the operators -- 5. The point spectrum of the problem -- 6. The essential spectrum -- References -- Influence of Linear Concentration Heat Source and Parabolic Density on Penetrative Convection Onset -- 1. Introduction -- 2. Basic equations and steady state solution -- 3. Onset of penetrative convection localization -- Acknowledgments -- References -- On Penetrative Convection in Porous Media Driven by Quadratic Sources -- 1. Introduction -- 2. Basic equations and steady state solution -- 3. Onset of penetrative convection -- Acknowledgments -- References -- Non-linear Schrodinger Equation in a Two-Fluid Plasma -- References -- The Non-Relativistic Limit of Relativistic Extended Thermodynamics with Many Moments. Part II: How it Includes the Mass Momentum and Energy Conservation -- 1. Introduction -- 2. The case with N odd and M even -- 3. The case with N even and M odd -- References -- Existence and Energy Conservation for the Boltzmann Equation -- 1. Introduction -- 2. A useful identity -- 3. Basic estimates -- 4. Existence of weak solutions for noncutoff potentials -- 5. Concluding remarks -- Acknowledgments -- References -- From the Big Bang to Future Complete Cosmologies -- 1. Introduction -- 2. Obstructions to future completeness -- 3. Cosmic censorship conjectures.

4. Results for global existence -- 5. S1 symmetric vacuum Einsteinian spacetimes -- 6. Behaviour near the singularity -- 7. Open problems -- Bibliography -- First Order Weak Nonlocality in Extended Thermodynamics of Rigid Heat Conductors -- 1. Introduction -- 2. Second Law and weakly nonlocal state spaces -- 3. Solutions of the entropy inequality in case of local state -- 4. Conclusions -- References -- A Semigroup of Solutions for the Degasperis-Procesi Equation -- 1. Introduction -- 2. Viscous Approximations and Compactness -- 3. Vanishing Viscosity: L2 Stability Estimate -- 4. Proof of Theorem 1.1 -- References -- Numerical Simulation of Magnetically Deflected Transferred Arc -- 1. Introduction -- 2. Modelling approach -- 3. Selected Numerical Results -- References -- A Note on Balance Laws for Slow and Fast Chemical Reactions -- 1. Introduction -- 2. Governing equations and thermodynamics features -- 3. Symmetrization and equilibrium subsystem -- References -- Integration of Partially Integrable Equations -- 1. Introduction -- 2. Mathematical formulation of the problem -- 3. Local separation of singlevaluedness and multivaluedness -- 4. Experimental and numerical evidence of missing solutions -- 5. Consequences of singlevaluedness (Painleve) -- 6. Consequences of meromorphy (Nevanlinna) -- 7. Summary and open problems -- Acknowledgments -- References -- On the Stability and Asymptotic Stability of Steady Solutions of the Navier-Stokes Equations in Unbounded Domains -- 1. Introduction -- 2. Notations -- 3. Results -- References -- Reflection and Transmission of Acceleration Waves in Isotropic Solids when a Strong Discontinuity Occurs -- 1. Introduction -- 2. Field equations -- 3. Transmitted and reflected waves -- References -- Instability of a Pre-Stressed Solid-Fluid Mixture -- 1. Introduction.

2. Preliminary and Balance Equations -- 3. Constitutive Equations -- References -- Some Further Considerations on the Galilean Relativity Principle in Extended Thermodynamics -- 1. Expositive part -- References -- Waves and Vibrations in a Solid of Second Grade -- 1. Introduction -- 2. Basic equations -- 3. On the nature of the microstructural parameter a1 -- 4. Finite amplitude transverse plane waves -- 5. Concluding remarks -- Acknowledgments -- References -- About the Large Time Behavior of Dissipative Equations when a priori Bounds are Slowly Growing -- 1. Introduction -- 2. Examples -- 3. Conclusion -- References -- Deformation Waves in Microstructured Solids and Dispersion -- 1. Introduction -- 2. Governing equations -- 3. Hierarchies of waves -- 4. Discussion -- Acknowledgements -- References -- An Allelopathic Competition with an External Toxicant Input -- 1. Introduction -- 2. The delayed quorum sensing model -- 3. Equilibria -- 4. Local stability properties -- 5. Survival of the producing population -- References -- Stability and Other Considerations for a Nonlinear Diffusion System -- 1. Introduction -- 2. Formulation Preliminaries -- 3. Remarks on Uniqueness and Non-Uniqueness of Steady States -- 4. Linear Stability Instability -- 5. Nonlinear Stability -- References -- Generalized Rarefaction Waves and Riemann Problem for a Class of Dissipative Hyperbolic Models -- 1. Introduction -- 2. An example of 2 X 2 system -- 3. Generalized rarefaction waves -- 4. Conclusions and final remarks -- Acknowledgments -- References -- An Equilibrium Point Regularization for the Chen System -- 1. Introduction -- 2. Nonlinear feedback control -- 3. Linear feedback control -- 4. Tracking -- References.

Nonclassical Symmetry Reductions of the Calogero-Degasperis-Fokas Equation in (2+1) Dimensions -- 1. Introduction -- 2. Nonclassical symmetries of the (2 + l)-dimensional CDF equation. -- 3. Symmetry reductions to ODE's -- 4. Conclusions -- References -- A Linear Instability Analysis of the Benard Problem for Deep Convection -- References -- Multicomponent Reactive Flows -- 1. Introduction -- 2. Governing equations -- 3. Transport coefficients -- 4. The Cauchy problem -- 5. Anchored waves -- 6. Numerical simulation -- 7. Conclusion and extensions -- References -- Non-linear Waves in Fluids Near the Critical Point -- 1. Introduction -- 2. Thermodynamic potentials near the critical point -- 3. Motions of a fluid near the critical point -- 4. Example of waves of a fluid near the critical point -- 5. Conclusion -- Acknowledgments -- References -- On Euler Closures for Reactive Boltzmann Equations -- 1. Introduction -- 2. The collision-dominated regime -- 3. Moment equations -- References -- On the Geomagnetic Direction Problem: A Nonexistence Result -- 1. Introduction -- 2. Hilbert space criterion -- 3. Nonexistence in the vicinity of single multipole fields -- References -- On the Models of Nonlocal Nonlinear Optics -- 1. Introduction -- 2. The nonlocal nonlinear Schrodinger equation. -- 3. Weak nonlocality and high frequency limit. -- Acknowledgments -- References -- Closure of the Balance Laws for Gaseous Mixtures Near Chemical Equilibrium -- 1. Introduction -- 2. Chemical and kinetic framework -- 3. Model equation -- 4. Transport properties -- References -- Chaotic Patterns in Lotka-Volterra Systems with Behavioral Adaptation -- 1. Introduction and the Model -- 2. The Equilibria -- 3. A Period-Adding Example -- References.

An Euler-Poisson Model Based on MEP for Holes in Semiconductors.