Elliptic and Parabolic Problems: Rolduc and Gaeta 2001 : Proceedings of the 4th European Conference Rolduc, Netherlands 18-22 June 2001 : Gaeta, Italy 24-28 September 2001

505 Pages·2002·17.438 MB·English

by  Josef Bemelmans

Elliptic and Parabolic
P R O B L E MS
Rolduc and Gaeta 2001
Ed/tors
Josef Bemelmans | Bernard Brighi | Alain _
Michel Chipot | Francis Conrad | Itai Shafrir
Vanda Valente | Giorgio Vergara-Caffarelli
Proceedings of the
E u r o p e an C o n f e r e n ce
/2i^ Proceedings of the
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European Conference
Elliptic and Parabolic
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RoLduc and Gaeta 2001
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European Conference
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Rolduc and Gaeta 2001
Rolduc, Netherlands • 18-22 June 2001
Gaeta, Italy • 24-28 September 2001
Editors
Josef Bemelmans
RWTH Aachen, Germany
Bernard Brighi
Alain Brillard
Universite de Haute Alsace, France
Michel Chipot
Universitdt Zurich, Switzerland
Francis Conrad
Universite Henri Poincare-Nancy 1, France
Itai Shafrir
Technion-IIT, Israel
Vanda Valente
IAC, CNR, Italy
Giorgio Vergara-Caffarelli
Universita di Roma "La Sapienza", Italy
V fe World Scientific
wB New Jersey • London • Singapore • Hong Kong
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Proceedings of the Fourth European Conference on
ELLIPTIC AND PARABOLIC PROBLEMS — ROLDUC AND GAETA 2001
Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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Preface
This book is a collection of texts from some conferences that were
given in Rolduc in June 2001 and Gaeta in September 2001, dur
ing the Fourth European Conference on Elliptic and Parabolic
Problems.
The subjects adressed in this volume are dealing with Calculus
of Variations, Free Boundary Problems, Homogenization, Model
ing, Numerical Analysis and various applications in physics, me
chanics and engineering.
We would like to thank all the participants to these meetings
for their help in making it successful. Special thanks go to the
contributors of this volume, and in particular to E. Maitre.
These meetings have been made possible by grants from the
IAC in Rome and from the Universities of Mulhouse, Nancy, Roma
"La Sapienza", Zurich, the RWTH of Aachen and the Technion
of Haifa. We express our deep appreciation to these institutions.
Finally, we thank World Scientific for helping us to publish these
proceedings.
J. Bemelmans, B. Brighi, A. Brillard, M. Chipot,
F. Conrad, I. Shafrir, V. Valente, G. Vergara-Cafarelli
V
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VII
CONTENTS
Preface v
1. Rolduc
Models for shape memory alloys described by subdifferentials of
indicator functions 1
T. Aiki and N. Kenmochi
Semilinear elliptic boundary value problems with critical Sobolev
exponent 11
C. Bandle
Diffraction problems for quasilinear elliptic and parabolic systems ... 21
G. Boyadjiev and N. Kutev
Extremality and compactness results for elliptic hemivariational
inequalities 30
S. Carl
On an operator equation for Stokes boundary value problems 40
T. D. Chandra and J. de Graaf
Local stability under changes of boundary conditions at a far
away location 52
M. Chipot and A. Rougirel
On some variational problems with an infinite number of wells 66
A. Elfanni
Boltzmann equation for quantum particles and Fokker Planck
approximation 75
M. Escobedo
Boundedness of global solutions of nonlinear parabolic equations .... 88
M. Fila
Transmission problems for degenerate parabolic equations 103
T. Fukao
Existence of solutions of a segregation model arising in population
dynamics 113
G. Galiano, M. L. Garzon and A. Jungel
The nonstationary Stokes and Navier-Stokes equations in
aperture domains 126
T. Hishida
viii
Global attractors for multivalued flows associated with
subdifferentials 135
N. Kenmochi and N. Yamazaki
Quasiconvex extreme points of convex sets 145
M. Kruzik
The Richards equation for the modeling of a nuclear waste
repository 152
0. Lafitte and C. Le Potier
Trace identities and universal estimates for eigenvalues of
linear pencils 160
M. Levitin and L. Parnovski
Universal estimates for the blow-up rate in a semilinear
heat equation 165
J. Matos and P. Souplet
Asymptotic behavior of curves evolving by forced curvature flows ... 175
H. Ninomiya
Existence of non-steady flows of an incompressible, viscous drop
of fluid in a frame rotating with finite angular velocity 180
M. Padula and V. A. Solonnikov
On a convection-diffusion equation with partial diffusivity 204
A. Pascucci
Quasiconvexity and optimal design 215
P. Pedregal
A regularity criterion for the angular velocity component in the
case of axi-symmetric Navier-Stokes equations 233
M. Pokorny
A comparison principle for the p-Laplacian 243
A. Poliakovsky and I. Shafrir
Supercritical variational problems with unique critical points 253
W. Reichel
Structure of the solution flow for steady-state problems of
one-dimensional Fremond models of shape memory alloys 263
K. Shirakawa
Lagrangian coordinates in free boundary problems for
multidimensional parabolic equations 274
S. I. Shrnarev
The Brezis-Nirenberg problem on Hn. Existence and uniqueness
of solutions 283
S. Stapelkamp
IX
Solvability of general elliptic problems in Holder spaces 291
V. Volpert and A. Volpert
2. Gaeta
Nonlinear diffusion in irregular domains 302
U. G. Abdulla
Analysis of radiative transfer equation coupled with nonlinear
heat conduction equation 311
F. Asllanaj, G. Jeandel, J. R. Roche and D. Schmitt
Viscosity Lyapunov functions for almost sure stability of
degenerate diffusions 322
M. Bardi and A. Cesaroni
Mass transport through charged membranes 332
D. Bothe and J. Priiss
The Hopf solution of Hamilton-Jacobi equations 343
/. C. Dolcetta
Conservation of critical groups in a weaker topology for
functionals associated with quasilinear elliptic equations 352
J. N. Corvellec and H. Douik
Approximating exterior flows by flows on truncated exterior
domains: piecewise polygonal artificial boundaries 364
P. Deuring
On the Stefan problem with surface tension 377
J. Escher, J. Priiss and G. Simonett
Epidemic models with compartmental diffusion 389
W. E. Fitzgibbon, M. Langlais and J. J. Morgan
Algebraic multigrid for selected PDE systems 399
T. Fullenbach and K. Stuben
Numerical computation of electromagnetic guided waves in a
general perturbed stratified medium 411
D. G. Pedreira
A non-stationary model for catalytic converters with cylindrical
geometry 424
J.-D. Hoernel
Exact controllability of piezoelectric shells 434
B. Miara
Optimal control approach for the fluid-structure interaction
problems 442
C. M. Murea