Asymptotic Methods in Nonlinear Wave Phenomena: In Honor of the 65th Birthday of Antonio Greco; Palermo, Italy, 5-7 June 2006

228 Pages·2007·9.03 MB·English

by  T. Ruggeri

Asymptotic Methods in
Nonlinear Wave
Phenomena
4
/iemwy"f/L. 65h& rtAhy
Antonio Greco
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Asymptotic Methods in
Nonlinear Wave
Phenomena
In Honor of the 65th birthday of
Antonio Greco
Palermo, Italy 5 - 7 June 2006
Editors
T Ruggeri
University of Bologna, Italy
M Sammartino
University of Palermo, Italy
1:
@World Scientific
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British Library Cataloguing-in-PublicationD ata
A catalogue record for this book is available from the British Library.
ASYMPTOTIC METHODS IN NONLINEAR WAVE PHENOMENA
In Honor of Antonio Greco on his 65th Birthday
Copyright Q 2007 by World Scientific Publishing Co. Re. Ltd.
All rights reserved. This book, or parts thereoi may not be reproduced in any form or by any means,
electronic 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-13 978-981-270-782-6
ISBN-10 981-270-782-4
Printed in Singapore by World Scientific Printers (S)P te Ltd
PREFACE
This volume is dedicated to Antonio Greco’s influence and achievements,
on his 65th birthday. It is an outgrowth from a conference on Asymptotic
Methods in Nonlinear Wave Phenomena which was held in his honor in
Mondello (Palermo) 5-7 June 2006.
Antonio has made significant contributions to the understanding of non-
linear propagation phenomena and to symmetry group methods applied to
PDEs arising in mathematical physics. Here we will just mention his re-
search on completely exceptional hyperbolic systems and Von Karman’s
fluids; asymptotic waves; the interaction between gravitational and acous-
tic waves in relativistic fluid dynamics and the completely integrability of
the generalized Kadomtsev-Petviashvili equation through the use of the
Painlev6 test and of the Lax pair.
His merit also includes the gathering in Palermo of a group of young
and enthusiastic researchers sharing his vision and scientific interests. We
believe that, under his leadership, this group will continue to grow and to
accomplish even more ambitious goals.
Antonio Greco has held several administrative responsibilities. He has
served as a Director of a CNR laboratory and is currently the Director of
the Math Department and also the Principal Investigator of the unit of
Palermo in the PRIN funding project. He has organized several successful
international conferences and taught twice, in 1982 and in 1986, at the
“Scuola Estiva di Fisica Matematica” in Ravello, the last being jointly
taught with our unforgetable colleague and friend, Andrea Donato.
It is also a pleasure to mention Antonio’s unique qualities which have
made him a special man. He has a bright personality, a generous nature
and it is always a pleasure being in his company.
We wish him all the best and to keep up the good work.
He will definitely remain as brotherly friend for the rest of our lives.
Tommaso Ruggeri and Marco Sammartino
January 2007
V
Professor Ankonio Creco
Universitk degli Studi di Palernro
SCIENTIFIC COMMITTEE
Chairman: T. Ruggeri (Bologna)
Y. Choquet-Bruhat (Parigi), S. Rionero (Napoli)
M. Sammartino (Palermo)
ORGANIZING COMMITTEE
Chairman: M. Sammartino (Palermo)
G. Gambino (Palermo), M. C. Lombard0 (Palermo),
V. Sciacca (Palermo), L. Seta (Palermo)
SUPPORTED BY
Universith degli Studi di Palermo
0
Gruppo Nazionale per la Fisica Matematica (G.N.F.M.)
0
dell’INdAM
MIUR PRIN 2003-05 Nonlinear Mathematical Problems of Wave
0
Propagation and Stability in Models of Continuous Media
vii
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
CONTENTS
Preface V
Conference Committees vii
The Semiconductor Steady Boltzmann Equation: A Variational
Formulation with an Application to Mobility 1
A.M. Anile, G. Ali, G. Mascali
Generating Multi State Cellular Automata by using Chua’s
“Universal Neuron” 12
E. Bilotta, G. Di Blasi, S. Giambd, P. Pantano
Isocline Curves and Variational Scalar Field 24
G. Boillat, A. Muracchini
Fokker-Planck Asymptotics and the Ricci Flow 35
M. Carfora
Exact Solutions of a Reaction Diffusion Equation 47
M. Carini, N. Manganaro
Some Applications of Linear Response Theory to Media with
Mechanical Relaxation Phenomena 58
A. Ciancio, V. Ciancio, F. Farsaci
Reduction of the Three-Wave Resonant Interaction to the
Sixth Painlev6 Equation 67
R. Conte, A.M. Grundland, M. Musette
The D’A lembert-Lagrange Principle for Gradient Theories
and Boundary Conditions 79
H. Gouin
ix