Bemelmans J. et. al. (editor) Elliptic and Parabolic Problems: Rolduc and Gaeta 2001

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Elliptic and Parabolic

PROBLEMS

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

European Conference

/2i^

Proceedings of the

^th

European Conference

Elliptic and Parabolic

'ROBLEM~

RoLduc and Gaeta 2001

This page is intentionally left blank

'4k

i-Mi Proceedings

the

European Conference

nW^»

Elliptic and Parabolic

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

Roma

"La Sapienza", Italy

Vfe World Scientific

wB New Jersey

•

London

•

Singapore

•

Hong Kong

Published by

World Scientific Publishing Co. Pte. Ltd.

P O Box 128, Farrer Road, Singapore 912805

USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661

UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

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

All rights

reserved.

This

book,

or parts

thereof,

may not be reproduced in any form or by any means,

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without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright

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ISBN 981-238-045-0

Printed by Fulsland Offset Printing (S) Pte Ltd, Singapore

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,

Conrad, I. Shafrir, V. Valente, G. Vergara-Cafarelli

This page is intentionally left blank

CONTENTS

VII

Preface v

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

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

Pascucci

Quasiconvexity and optimal design 215

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

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 H

. Existence and uniqueness

of solutions 283

S. Stapelkamp

Solvability of general elliptic problems in Holder spaces 291

V. Volpert and A. Volpert

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

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

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

G. Pedreira

A non-stationary model for catalytic converters with cylindrical

geometry 424

J.-D.

Hoernel

Exact controllability of piezoelectric shells 434

Miara

Optimal control approach for the fluid-structure interaction

problems 442

C. M. Murea