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Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathema- ciansfromtheSt.PetersburgMathematicalSchool.Hisremarkableresultsonexact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, and Stokes systems, his methods and contributions to the - vestigation of free boundary problems, in particular in ?uid mechanics, are well known to specialists all over the world. The International Conference on Trends in Partial Di?erential Equations of th Mathematical Physics was held on the occasion of his 70 birthday in Obidos (Portugal), from June 7 to 10, 2003. It was an organization of the Centro de Matem atica e Aplica c oes Fundamentais da Universidade Lisboa , in collaboration with the Centro de Matem atica da Universidade de Coimbra , the Centro de Matem atica Aplicada do IST/Universidade T ecnica de Lisboa , the Centro de Matem atica da Universidade da Beira Interior ,from Portugal,and with the L- oratory of Mathematical Physics of the St.Petersburg Department of the Steklov Institute of Mathematics from Russia. The conference consisted of thirty eight invited and contributed lectures and gathered,inthecharminganduniquemedievaltownofObidos,aboutsixtypart- ipants from ?fteen countries, namely USA, Switzerland, Spain, Russia, Portugal, Poland, Lithuania, Korea, Japan, Italy, Germany, France, Canada, Australia and Argentina.Severalcolleaguesgaveusahelpinghandintheorganizationofthec- ference. We are thankful to all of them, and in particular to Stanislav Antontsev, Anvarbek Meirmanov and Ad elia Sequeira, that integrated also the Organizing Committee. A special acknowledgement is due to Elena Frolova that helped us in compiling the short and necessarily incomplete bio-bibliographical notes below.
List of contents
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 L 2-spaces and Strong Solutions of the Navier-Stokes Equations in .- A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity.- On the 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 Bénard 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.
