Applied Nonlinear Analysis

This book is meant as a present to honor Professor on the th occasion of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from eleven countries. They cover many different areas of research related to the work of Professor including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions of parabolic and elliptic problems, operator theory and numerical methods. The realization of this book could not have been made possible without the generous support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. Special thanks are due to Dr. Ulrych for the careful preparation of the final version of this book. Last but not least, we wish to express our gratitude to Dr. for her invaluable assistance from the very beginning. This project could not have been successfully concluded without her enthusiasm and loving care for her father. On behalf of the editors ADÉLIA SEQUEIRA v honored by the Order of Meritof the Czech Republic by Václav Havel, President of the Czech Republic, on the October 28, 1998, Professor Emeritus of Mathematics at the Charles University in Prague, Presidential Research Professor at the Northern Illinois University and Doctor Honoris Causa at the Technical University of Dresden, has been enriching the Czech and world mathematics with his new ideas in the areas of partial differential equations, nonlinear functional analysis and applications of the both disciplines in continuum mechanics and hydrodynamics for more than forty years.

Table of Contents:
On the Regularity and Decay of the Weak Solutions to the Steady-State Navier-Stokes Equations in Exterior Domains.- A Note on Turbulence Modeling.- L2,?-Regularity for Nonlinear Elliptic Systems of Second Order.- On the Fredholm Alternative for Nonlinear Homogeneous Operators.- Existence of Solutions to a Nonlinear Coupled Thermo-Viscoelastic Contact Problem with Small Coulomb Friction.- On Some Global Existence Theorems for a Semilinear Parabolic Problem.- Bifurcation of Solutions to Reaction-Diffusion Systems with Jumping Nonlinearities.- Coupled Problems for Viscous Incompressible Flow in Exterior Domains.- Remarks on the Determinant in Nonlinear Elasticity and Fracture Mechanics.- On Modelling of Czochralski Flow, the Case of Non Plane Free Surface.- Symmetric Stationary Solutions to the Plane Exterior Navier-Stokes Problem for Arbitrary Large Reynolds Number.- A Fictitious-Domain Method with Distributed Multiplier for the Stokes Problem.- Reliable Solution of a Unilateral ContactProblem with Friction, Considering Uncertain Input Data.- Domain Decomposition Algorithm for Computer Aided Design.- Solution of Convection-Diffusion Problems with the Memory Terms.- On Global Existence of Smooth Two-Dimensional Steady Flows for a Class of Non-Newtonian Fluids under Various Boundary Conditions.- Viscosity Solutions for Degenerate and Nonmonotone Elliptic Equations.- Remarks on Compactness in the Formation of Fine Structures.- Finite Element Analysis of a Nonlinear Elliptic Problem with a Pure Radiation Condition.- Estimates of Three-Dimensional Oseen Kernels in Weighted LP Spaces.- Hardy’s Inequality and Spectral Problems of Nonlinear Operators.- Remarks on the Regularity of Solutions of Elliptic Systems.- Singular Perturbations in Optimal Control Problem.- Optimization of Steady Flows for Incompressible Viscous Fluids.- Asymptotic Behaviour of Compressible Maxwell Fluids in Exterior Domains.- Regularity of a Suitable Weak Solution to the Navier-Stokes Equations as a Consequence of Regularity of One Velocity Component.- On a Class of High Resolution Methods for Solving Hyperbolic Conservation Laws with Source Terms.- On the Decay to Zero of the L2-Norms of Perturbations to a Viscous Compressible Fluid Motion Exterior to a Compact Obstacle.- Global Behavior of Compressible Fluid with a Free Boundary and Large Data.- A Geometric Approach to Dynamical Systems in ?N.- On a Three-Dimensional Convective Stefan Problem for a Non-Newtonian Fluid.- Replacing H by H2.- Flow of Shear Dependent Electrorheological Fluids: Unsteady Space Periodic Case.- On Decay of Solustions to the Navier-Stokes Equations.- Convexity Conditions for Rotationally Invariant Functions in Two Dimensions.- Hölder Continuity of Weak Solutions to Certain Nonlinear Parabolic Systems in Two Space Dimensions.