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

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

H. Abels

Bounded Imaginary Powers and H∞-Calculus of

the Stokes Operator in Unbounded Domains . . . . . . . . . . . . . . . . . . . . . . . . 1

M. Borsuk and A. Zawadzka

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

D. Bothe, J. Pr¨uss and G. Simonett

Well-posedness of a Two-phase Flow with Soluble Surfactant . . . . . . . . 37

J. Brasche and M. Demuth

Resolvent Differences for General Obstacles . . . . . . . . . . . . . . . . . . . . . . . . . 63

J.I. D´ıaz

Special Finite Time Extinction in Nonlinear Evolution

Systems: Dynamic Boundary Conditions and

Coulomb Friction Type Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

M. Duelli and L. Weis

Spectral Projections, Riesz Transforms and

H∞-calculus for Bisectorial Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

R. Farwig, G.P. Galdi and H. Sohr

Very Weak Solutions of Stationary and Instationary

Navier-Stokes Equations with Nonhomogeneous Data . . . . . . . . . . . . . . . 113

M. Fila, J.J.L. Vel´azquez and M. Winkler

Grow-up on the Boundary for a Semilinear Parabolic Problem . . . . . . 137

H. Gajewski and I.V. Skrypnik

Existence and Uniqueness Results for Reaction-diffusion Processes

of Electrically Charged Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

F. Colombo and D. Guidetti

An Inverse Problem for a Phase-field Model in Sobolev Spaces . . . . . . 189

vi Contents

O. Anza Hafsa and M. Chipot

Numerical Analysis of Microstructures:

The Influence of Incompatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

J. Hern´andez, F.J. Mancebo and J.M. Vega

Nonlinear Singular Elliptic Problems:

Recent Results and Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

M. Hieber

The Navier-Stokes Flow in the Exterior of Rotating Obstacles . . . . . . . 243

M. Kuˇcera, J. Eisner and L. Recke

A Global Bifurcation Result for Variational Inequalities . . . . . . . . . . . . . 253

P.C. Kunstmann

On Elliptic Non-divergence Operators with

Measurable Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

P. Lauren¸cot and D. Wrzosek

A Chemotaxis Model with Threshold Density and

Degenerate Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

J. L´opez-G´omez and M. Molina-Meyer

In the Blink of an Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

J. L´opez-G´omez and C. Mora-Corral

Generalized Minimal Cardinal of the λ-slices of the Semi-bounded

Components Arising in Global Bifurcation Theory . . . . . . . . . . . . . . . . . . 329

S.A. Messaoudi

Blow-up of Solutions of a Semilinear Heat Equation with

a Visco-elastic Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

C.M. Murea and G. Hentschel

Finite Element Methods for Investigating the Moving

Boundary Problem in Biological Development . . . . . . . . . . . . . . . . . . . . . . . 357

J. Naumann

Existence of Weak Solutions to the Equations of Stationary

Motion of Heat-conducting Incompressible Viscous Fluids . . . . . . . . . . . 373

P. Pol´aˇcik and P. Quittner

Liouville Type Theorems and Complete Blow-up for

Indefinite Superlinear Parabolic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 391

D. Praˇz´ak

On Reducing the 2d Navier-Stokes Equations to

a System of Delayed ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

J. Rehberg

Quasilinear Parabolic Equations in Lp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

Contents vii

A. Rodr´ıguez-Bernal

Parabolic Equations in Locally Uniform Spaces . . . . . . . . . . . . . . . . . . . . . 421

B. Scarpellini

Bifurcation of Traveling Waves Related to the B´enard Equations

with an Exterior Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

H.-J. Schmeißer and W. Sickel

Vector-valued Sobolev Spaces and

Gagliardo-Nirenberg Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

P. Souplet

The Influence of Gradient Perturbations on Blow-up Asymptotics in

Semilinear Parabolic Problems: A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

Kenichiro Umezu

Non-existence of Positive Solutions for Diffusive Logistic Equations

with Nonlinear Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

A. Rodr´ıguez-Bernal and A. Vidal-L´opez

Extremal Equilibria and Asymptotic Behavior of

Parabolic Nonlinear Reaction-diffusion Equations . . . . . . . . . . . . . . . . . . . 509

C. Walker

A Remark on Continuous Coagulation-Fragmentation Equations

with Unbounded Diffusion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

P. Weidemaier

On Lp-Estimates of Optimal Type for the Parabolic Oblique

Derivative Problem with VMO-Coefficients – A Refined Version . . . . . 529