Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann

ISBN-13: 9783764372668 / Angielski / Twarda / 2005 / 536 str.

Michel Chipot; Joachim Escher

Opis

The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann.
The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.

Recenzje

From the reviews:

“This book is a collection of 32 articles and is meant as a special tribute to the work of H. Amann of the University Zuerich on the occasion of his retirement. It is an interesting mix at the boundary between pure and applied mathematics. … This is an interesting collection, since it contains papers which one does not see if one is not a specialist and therefore gives a motivating fresh look on certain subjects.” (M. Hofmann-Ostenhof, Monatshefte für Mathematik, Vol. 152 (1), September, 2007)

Spis treści

Bounded Imaginary Powers and H?-Calculus of the Stokes Operator in Unbounded Domains.- Exact Estimates of Solutions to the Robin Boundary Value Problem for Elliptic Non-divergent Second-order Equations in a Neighborhood of the Boundary Conical Point.- Well-posedness of a Two-phase Flow with Soluble Surfactant.- Resolvent Differences for General Obstacles.- Special Finite Time Extinction in Nonlinear Evolution Systems: Dynamic Boundary Conditions and Coulomb Friction Type Problems.- Spectral Projections, Riesz Transforms and H?-calculus for Bisectorial Operators.- Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data.- Grow-up on the Boundary for a Semilinear Parabolic Problem.- Existence and Uniqueness Results for Reaction-diffusion Processes of Electrically Charged Species.- An Inverse Problem for a Phase-field Model in Sobolev Spaces.- Numerical Analysis of Microstructures: The Influence of Incompatibility.- Nonlinear Singular Elliptic Problems: Recent Results and Open Problems.- The Navier-Stokes Flow in the Exterior of Rotating Obstacles.- A Global Bifurcation Result for Variational Inequalities.- On Elliptic Non-divergence Operators with Measurable Coefficients.- A Chemotaxis Model with Threshold Density and Degenerate Diffusion.- In the blink of an Eye.- Generalized Minimal Cardinal of the ?-slices of the Semi-bounded Components Arising in Global Bifurcation Theory.- Blow-up of Solutions of a Semilinear Heat Equation with a Visco-elastic Term.- Finite Element Methods for Investigating the Moving Boundary Problem in Biological Development.- Existence of Weak Solutions to the Equations of Stationary Motion of Heat-conducting Incompressible Viscous Fluids.- Liouville Type Theorems and Complete Blow-up for Indefinite Superlinear Parabolic Equations.- On Reducing the 2d Navier-Stokes Equations to a System of Delayed ODEs.- Quasilinear Parabolic Equations in Lp.- Parabolic Equations in Locally Uniform Spaces.- Bifurcation of Traveling Waves Related to the Bénard Equations with an Exterior Force.- Vector-valued Sobolev Spaces and Gagliardo-Nirenberg Inequalities.- The Influence of Gradient Perturbations on Blow-up Asymptotics in Semilinear Parabolic Problems: A Survey.- Non-existence of Positive Solutions for Diffusive Logistic Equations with Nonlinear Boundary Conditions.- Extremal Equilibria and Asymptotic Behavior of Parabolic Nonlinear Reaction-diffusion Equations.- A Remark on Continuous Coagulation-Fragmentation Equations with Unbounded Diffusion Coefficients.- On Lp-Estimates of Optimal Type for the Parabolic Oblique Derivative Problem with VMO-Coefficients — A Refined Version.