On November 3, 2005, Alexander Vasil'evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov's contributions to science is provided in the following article "Scienti?c portrait of Alexander Vasil'evich Kazhikhov". This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.

"The scientific interests of Professor A.V. Kazhikhov were fundamentally devoted to Mathematical Fluid Mechanics, where he achieved outstanding results that had, and still have, a significant influence on this field.This volume, dedicated to the memory of A.V. Kazhikhov, presents the latest contributions from renowned world specialists in a number of new important directions of Mathematical Physics, mostly of Mathematical Fluid Mechanics, and, more generally, in the field of nonlinear partial differential equations. These results are mostly related to boundary value problems and to control problems for the Navier-Stokes equations, and for equations of heat convection. Other important topics include non-equilibrium processes, Poisson-Boltzmann equations, dynamics of elastic body, and related problems of function theory and nonlinear analysis. TOC:Scientific Portrait of A.V. Kazhikhov.- Boundary Control Problems for Stationary Equations of Heat Convection.- Homogenization of the Poisson-Boltzmann Equation.- Superconducting Vortices: Chapman Full Model.- Augmented Lagrangian Method and Compressible Visco-plastic Flows: Applications to Shallow Dense Avalanches.- Oscillatory Limits with Changing Eigenvalues.- Finite-dimensional Control for the Navier-Stokes Equations.- On the Sharp Vanishing Viscosity Limit of Viscous Incompressible Fluid Flows.- Small Péclet Number Approximation as a Singular Limit of the Full Navier-Stokes-Fourier System with Radiation.- New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner.- Existence of a Regular Periodic Solution to the Rothe Approximation of the Navier-Stokes Equation in Arbitrary Dimension.- Optimal Neumann Control for the 2-D Steady-state Navier-Stokes equations.- On Some Boundary Value Problem for the Stokes Equations with a Parameter in an Infinite Sector.- Unilateral Contact Problems Between an Elastic Plate and a Beam.- On Lighthill's Acoustic Analogy for Low Mach Number Flows.- On the Uniqueness of Solutions to Boundary Value Problems for Non-stationary Euler Equations.- On Nonlinear Stability of MHD Equilibrium Figures.- Viscous Flows in Domains with a Multiply Connected Boundary.- Problems with Insufficient Information about Initial-boundary Data.- On the Stability of Non-symmetric Equilibrium Figures of Rotating Self-gravitating Liquid not Subjected to Capillary Forces.- Dynamics of a Non-fixed Elastic Body."

Boundary Control Problems for Stationary Equations of Heat Convection.- Homogenization of the Poisson-Boltzmann Equation.- Superconducting Vortices: Chapman Full Model.- Augmented Lagrangian Method and Compressible Visco-plastic Flows: Applications to Shallow Dense Avalanches.- Oscillatory Limits with Changing Eigenvalues: A Formal Study.- Finite-dimensional Control for the Navier-Stokes Equations.- On the Sharp Vanishing Viscosity Limit of Viscous Incompressible Fluid Flows.- Small Péclet Number Approximation as a Singular Limit of the Full Navier-Stokes-Fourier System with Radiation.- New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner.- Existence of a Regular Periodic Solution to the Rothe Approximation of the Navier-Stokes Equation in Arbitrary Dimension.- Optimal Neumann Control for the Two-dimensional Steady-state Navier-Stokes equations.- On Some Boundary Value Problem for the Stokes Equations with a Parameter in an Infinite Sector.- Unilateral Contact Problems Between an Elastic Plate and a Beam.- On Lighthill's Acoustic Analogy for Low Mach Number Flows.- On the Uniqueness of Solutions to Boundary Value Problems for Non-stationary Euler Equations.- On Nonlinear Stability of MHD Equilibrium Figures.- Viscous Flows in Domains with a Multiply Connected Boundary.- Problems with Insufficient Information about Initial-boundary Data.- On the Stability of Non-symmetric Equilibrium Figures of Rotating Self-gravitating Liquid not Subjected to Capillary Forces.- Dynamics of a Non-fixed Elastic Body.