Nonlinear Elliptic And Parabolic Problems

by Chipot, Michel; Escher, Joachim

• ISBN13: 9783764372668
• ISBN10: 3764372664
• Format: Hardcover
• Copyright: 2006-01-30
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface	ix
Bounded Imaginary Powers and H∞-Calculus of the Stokes Operator in Unbounded Domains	1	(16)
H. Abels
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	17	(20)
M. Borsuk
A. Zawadzka
Well-posedness of a Two-phase Flow with Soluble Surfactant	37	(26)
D. Bothe
J. Pruss
G. Simonett
Resolvent Differences for General Obstacles	63	(8)
J. Brasche
M. Demuth
Special Finite Time Extinction in Nonlinear Evolution Systems: Dynamic Boundary Conditions and Coulomb Friction Type Problems	71	(28)
J.I. Diaz
Spectral Projections, Riesz Transforms and H∞-calculus for Bisectorial Operators	99	(14)
M. Duelli
L. Weis
Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data	113	(24)
R. Farwig
G.P. Galdi
H. Sohr
Grow-up on the Boundary for a Semilinear Parabolic Problem	137	(14)
M. Fila
J.J.L. Velazquez
M. Winkler
Existence and Uniqueness Results for Reaction-diffusion Processes of Electrically Charged Species	151	(38)
H. Gajewski
I.V. Skrypnik
An Inverse Problem for a Phase-field Model in Sobolev Spaces	189	(22)
F. Colombo
D. Guidetti
Numerical Analysis of Microstructures: The Influence of Incompatibility	211	(16)
O. Anza Hafsa
M. Chipot
Nonlinear Singular Elliptic Problems: Recent Results and Open Problems	227	(16)
J. Hernandez
F.J. Mancebo
J.M. Vega
The Navier-Stokes Flow in the Exterior of Rotating Obstacles	243	(10)
M. Hieber
A Global Bifurcation Result for Variational Inequalities	253	(12)
M. Kucera
J. Eisner
L. Recke
On Elliptic Non-divergence Operators with Measurable Coefficients	265	(8)
P.C. Kunstmann
A Chemotaxis Model with Threshold Density and Degenerate Diffusion	273	(18)
P. Laurencot
D. Wrzosek
In the Blink of an Eye	291	(38)
J. Lopez-Gomez
M. Molina-Meyer
Generalized Minimal Cardinal of the λ-slices of the Semi-bounded Components Arising in Global Bifurcation Theory	329	(22)
J. Lopez-Gomez
C. Mora-Corral
Blow-up of Solutions of a Semilinear Heat Equation with a Visco-elastic Term	351	(6)
S.A. Messaoudi
Finite Element Methods for Investigating the Moving Boundary Problem in Biological Development	357	(16)
C.M. Murea
G. Hentschel
Existence of Weak Solutions to the Equations of Stationary Motion of Heat-conducting Incompressible Viscous Fluids	373	(18)
J. Naumann
Liouville Type Theorems and Complete Blow-up for Indefinite Superlinear Parabolic Equations	391	(12)
P. Polacik
P. Quittner
On Reducing the 2d Navier-Stokes Equations to a System of Delayed ODEs	403	(10)
D. Prazak
Quasilinear Parabolic Equations in LP	413	(8)
J. Rehberg
Parabolic Equations in Locally Uniform Spaces	421	(12)
A. Rodriguez-Bernal
Bifurcation of Traveling Waves Related to the Benard Equations with an Exterior Force	433	(30)
B. Scarpellini
Vector-valued Sobolev Spaces and Gagliardo-Nirenberg Inequalities	463	(10)
H.-J. Schmeißer
W. Sickel
The Influence of Gradient Perturbations on Blow-up Asymptotics in Semilinear Parabolic Problems: A Survey	473	(24)
P. Souplet
Non-existence of Positive Solutions for Diffusive Logistic Equations with Nonlinear Boundary Conditions	497	(12)
Kenichiro Umezu
Extremal Equilibria and Asymptotic Behavior of Parabolic Nonlinear Reaction-diffusion Equations	509	(8)
A. Rodriguez-Bernal
A. Vidal-Lopez
A Remark on Continuous Coagulation-Fragmentation Equations with Unbounded Diffusion Coefficients	517	(12)
C. Walker
On LP-Estimates of Optimal Type for the Parabolic Oblique Derivative Problem with VMO-Coefficients -- A Refined Version	529
P. Weidemaier