Acoustics, Mechanics, and the Related Topics of Mathematical flnalqsis This page intentionally left blank Proceedings of the International Conference to Celebrate Robert P. Gilbert's 70th Birthday Acoustics, Mechanics, and the Related Topics of Mathema tical Analqsis CAES du CNRS, Frejus, France 18 - 22 June 2002 Editor Armand Wirgin Laboratoire de Mecanique et dAcoustique Marseille, France orld Scientific Jersey London Singapore Hong Kong Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofice: Suite 202,1060 Main Street, River Edge, NJ 07661 UK ofice: 57 Shelton Street, Covent Garden, London WCZH 9HE British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library. ACOUSTICS, MECHANCIS, AND THE. RELATED TOPICS OF MATHEMATICAL ANALYSIS Proceedings of the International Conference to Celebrate Robert P. Gilbert’s 70th Birthday Copyright 0 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, eZectronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-238-264-X This book is printed on acid-free paper. Printed in Singapore by Mainland Press PREFACE The international conference Acoustics, Mechanics, and the Related Topics of Mathematical Analysis (AMRTMA) was held on 18-22 June, 2002 at the Villa Clythia, CAES du CNRS, in Frbjus, France. This interdis- ciplinary meeting was in some respects a smaller-format copy of previous ISAAC conferences. AMRTMA was sponsored jointly by the Rbgion PACA (Provence Alpes CBte d’Azur), the CNRS (Centre National de la Recherche Scientifique) and ISAAC (International Society for Analysis, its Applica- tions and Computation). The objective of AMRTMA was two-fold. First, and above all, it was the occasion for friends and admirers of Robert P. Gilbert to celebrate his 70th birthday in a convivial atmosphere. Second, the conference was to Figure 1. Bob Gilbert on the boat to St. Tkopez during the AMRTMA conference provide a means for bringing together scientists from many different fields to discuss the intricacies and usefulness of applied mathematics, notably in the realm of mechanics. A group of over 60 persons, composed of scholars, scientists, engineers (some with their Spouses/companions and children) from the USA, Rance, Ger- many, Belgium, Italy, Greece, Austria, England, Sweden, Russia, Ukraine, Algeria, Tunisia and China, participated in this event. The quality of the (all half-hour) scientific communications (most of which appear in extenso V vi in this book) was high and the banquet in honor of R. Gilbert a memorable birthday celebration. As the participants were together (all lodged in the Villa Clythia, a vacation and conference facility of the CNRS) most of the time during the five days of the meeting, they had many occasions (notably during the meals, cocktails, and boat trip to St. Tropez) to socialize as well as exchange ideas and impressions. I would like to express my gratitude to the Centre National de la Recherche Scientifique, G. Berger, Directrice and E. Brun, Administrateur DkleguB, to the Conseil Wgional Provence-Alpes-C8te d’Azur, M. Hayot, Vice- PrBsident, to the International Society for Analysis, its Applications and Computation, H. Begehr, President of the Board, R.P. Gilbert, Member of the Board, and to the Laboratoire de MBcanique et d’Acoustique, M. Ritous, Directeur for their financial support and/or encouragement. The Scientific Committee members: A. Ben-Israel , Rutgers Univ., USA, A.-S. Bonnet Ben-Dhia, ENSTA, France, A. Bourgeat , Univ. St. Eti- enne, fiance, J. Buchanan, US Naval Acad., USA, C. Depollier, LAUM, fiance, R.P. Gilbert, Univ. Delaware, USA, G. Hile, Univ. Hawaii, USA, A. Jeffrey, Univ. Newcastle/Tyne, U.K., G. Maugin, LMM/CNRS/UPMC, fiance, F. Nicolosi, Univ. Catania, Italy, A. Panchenko, Penn State Univ., USA, A. Wirgin, LMA/CNRS, France, and Y. Xu, Univ. Tennessee, USA did a great job in selecting the communications and reviewing the papers for the proceedings book. The Organization Committee comprised of: G. Hile, Univ. Hawdi, USA, C. Tsogka, LMA/CNRS, France and A. Wirgin, LMA/CNRS, France acted efficiently in setting up the conference. I. Czyz, DBlCgation RBgionale du CNRS, Marseille, France provided pre- cious help on budgetary and financial issues, M. Morano, LMA/CNRS acted efficiently for the secretarial tasks, and E. Ogam, LMA/CNRS helped solve many problems connected with audiovisual presentations and informatics. My old friend R. Tanteri from Toulouse, France, made the web page that helped draw attention to the conference and A. DBlinibre LMA/CNRS, France installed this page on the LMA web site. The task of designing the logo of the conference was submitted to P. de Sentenac, Paris, France and to V. Quesnel, Rouen, fiance (whose design was finally retained). vii The success of the conference was largely due to the efforts of the kind and efficient personnel of the Villa Clythia: its Director, M. Chevalier, its Assistant Director, E. Porcu, and all the other members of the staff who made our stay an enjoyable experience. I wholeheartedly thank these many persons for their precious help. Next to last, but not least, I thank my wife Nicole and my daughter Zo6 for their encouragements and efficient help at the reception desk of the confer- ence. As concerns this book, I acknowledge the helpful aid and initiatives of Daniel Cartin and Chelsea Chin from World Scientific. Armand Wirgin This page intentionally left blank Contents Preface V A. Wirgin Paen R.P. Gilbert 1 R. Carroll About Bob Gilbert 4 A. Wirgin 8 Representation formulas in Clifford analysis H. Begehr Imaging methods in random media 14 J. Berryman, L. Borcea, G. Papanicolaou and C. Tsogka Resonances of an elastic plate in a duct, in the presence of a uniform 21 flow AS. Bonnet-Ben Dhia and J.-F. Mercier First order asymptotic modeling of a nuclear waste repository 28 A. Bourgeat, I. Boursier, 0. Gipoulowc and E. Marusic-Paloka Exact axisymmetric solution for temperature-dependent compressible 34 Navier-Stokes Equations P. Broadridge and T.M. Barrett Recovery of the poroelastic parameters of cancellous bone using low 41 frequency acoustic interrogation J.L. Buchanan, R.P. Gilbert and K. Khashanah Mathematical model of the interaction problem between 48 electromagnetic field and elastic body F. Cakoni and G.C. Hsiao Bore evolution in inhomogeneous channels 55 J. G. Caputo and Y.A. Stepanyants An inverse spectral problem for a Schrodinger operator with an 64 unbounded potential L. Cardoulis, M. Cristofol and P. Gaitan ix X Trapping regions for discontinuously coupled dynamic systems 71 S. Carl and J. W. Jerome Differential calculi 78 R. Carroll Reconstruction problem for a periodic boundary between two media 85 J. Chandezon, A. Ye. Poyedinchuk and N.P. Yashina. A note on generalized Cesho operators 92 D.C. Chang, R. Gilbert and G. Wang On the boundedness of functions from an anisotropic weighted space 100 satisfying some integral inequalities P. Cianci Homogenizing a flow of an incompressible inviscid fluid through 108 an elastic porous media T. Clopeau and A. Mickelic Approximation of a dynamic unilateral contact problem for a cracked 116 viscoelastic body M Cocou and G. Scarella Principles of signal based ray tracing for 2D and 3D complex tectonics 123 P. Cristini and E. De Bazelaire Regularity up to the boundary for a class of solutions of a functional- 130 differential system S. D 'Asero On the Hardy spaces of harmonic and monogenic functions in the unit 137 ball of R~+~ R. Delanghe Time domain wave equations for lossy media obeying a frequency 143 power law: application to the porous materials Z.E.A. Fellah, S. Berger, W. Lauriks and C. Depollier xi A model for porous ductile viscoplastic solids including void shape 150 effects L. Flandi and J. B. Leblond Acoustic wave propagation in a composite of two different poroelastic 157 materials with a very rough periodic interface: a homogenization approach R. Gilbert and MJ. Ou Effective acoustic equations for a nonconsolidated medium with 164 microstructure R.P. Gilbert andA. Panchenko A domain decomposition method for the Helmholtz equation in an 171 unbounded waveguide N. Gmati and N. Zrelli Support function method for inverse obstacle scattering problems 178 S. Gutman andA.G. Ramm Heat polynomial analogs 185 G.N. Hile and A. Stanoyevitch Blow-up, shock formation, and acceleration waves in hyperelastic 192 media A. Jeffrey Summability of solutions of Dirichlet problem 199 A. Kovalevsky and F. Nicolosi On isophonic surfaces 207 R. Magnanini A survey of pointwise interpolation inequalities for integer and 212 fractional derivatives V. Maz )a and T. Shaposhnikova Non-uniqueness in connection with methods for the reconstruction of 222 the shape of cylindrical bodies from acoustic scattering data E. Ogam, T. Scotti and A. Wirgin xii Dispersion identification using the Fourier analysis of resonances in 229 elastic and viscoelastic rods R. Othman, G. Gary, R. Blanc, M.N. Bussac and P. Collet Application of the likelihood method to the analysis of waves in elastic 236 and viscoelastic rods R. Othman, G. Gary, M.N. Bussac and P. CoIlet On the controlled evolution of level sets and like methods: the shape 243 and contrast reconstruction C. Ramananjaona, M. Lambert, D. Lesselier and J-P. Zol&o Recent progress in the theoretical and numerical modeling of thin-layer 25 1 flow L. Schwartz Seismic response in a city 258 C.