Rodrigues J.-F., Seregin G., Urbano J.M. (Eds.) Trends in Partial Differential Equations of Mathematical Physics

Birkhäusеr Bаsel, 2005, 282 pagesVsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable results on exact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, Stokes and Navier-Stokes systems, his methods and contributions to the inverstigation of free boundary problems, in particular in fluid mechanics, are well known to specialists all over the world.
The International Conference on "Trends in Partial Differential Equations of Mathematical Physics" was held on the occasion of his 70th birthday in Óbidos (Portugal) from June 7 to 10, 2003. The conference consisted of thirty-eight invited and contributed lectures and gathered, in the charming and unique medieval town of Óbidos, about sixty participants from fifteen countries.
This book contains twenty original contributions on many topics related to V.A. Solonnikov's work, selected from the invited talks of the conference.Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing
Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian
Weighted L2-spaces and Strong Solutions of the Navier-Stokes Equations in R3
A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity
Problem of Thermocapillary Convection for Two Incompressible Fluids Separated by a Closed Interface
Some Mathematical Problems in Visual Transduction
Global Regularity in Sobolev Spaces for Elliptic Problems with p-structure on Bounded Domains
Temperature Driven Mass Transport in Concentrated Saturated Solutions
Solvability of a Free Boundary Problem for the Navier-Stokes Equations Describing the Motion of
Viscous Incompressible Nonhomogeneous Fluid
Duality Principles for Fully Nonlinear Elliptic Equations
On the Benard Problem
Exact Boundary Controllability for Quasilinear Wave Equations
Regularity of Euler Equations for a Class of Three-Dimensional Initial Data
A Model of a Two-dimensional Pump
Regularity of a Weak Solution to the Navier-Stokes Equation in Dependence on Eigenvalues and Eigenvectors of the Rate of Deformation Tensor
Free Work and Control of Equilibrium Configurations
Stochastic Geometry Approach to the Kinematic Dynamo Equation of Magnetohydrodynamics
Quasi-Lipschitz Conditions in Euler Flows
Interfaces in Solutions of Diffusion-absorption Equations in Arbitrary Space Dimension
Estimates for Solutions of Fully Nonlinear Discrete Schemes