Ames W.F., Harrel E.M., Herod J.V. (editors). Differential Equations with Applications to Mathematical Physics
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Differential Equations with
Applications
to
Mathematical Physics
This
is
volume
192
in
MATHEMATICS IN SCIENCE
AND
ENGINEERING
Edited
by
William
F.
Ames,
Georgia Institute
of
Technology
A
list
of
recent titles in this series appears
at
the end
of
this volume.
Differential Equations with
Applications to
Mathematical Physics
Edited by
W.
I?
Ames
E.
M.
Harrell
II
J.
I?
Herod
SCHOOL
OF
MATHEMATICS
GEORGIA INSTITUTE
OF
TECHNOLOGY
ATLANTA, GEORGIA
ACADEMIC PRESS, INC.
Harcourt Brace Jouanouich, Publishers
Boston San Diego New York
London Sydney Tokyo Toronto
This
book
is printed on acid-free paper.
Q
Copyright
0
1993
by Academic Press, Inc.
All rights reserved.
No part of this publication may be reproduced or
transmitted in any form or by any means, electronic
or mechanical, including photocopy, recording, or
any information storage and retrieval system, without
permission in writing from the publisher.
ACADEMIC PRESS, INC.
1250
Sixth Avenue, San Diego, CA
92101-4311
United Kingdom edition published by
ACADEMIC PRESS LIMITED
24-28
Oval Road, London NW17DX
Library of Congress Cataloging-in-Publication Data
Differential equations with applications
to
mathematical physics
/
edited by
W.F.
Ames, E.M. Harrell
II,
J.V.
Herd.
Includes bibliographical references and index.
ISBN
0-
12-056740-7 (acid-fiee)
p.
cm.
-
(Mathematics
in
science and engineering
;
v.
192)
1.
Differential equations. 2. Mathematical physics.
I.
Ames,
William
F.
II.
Harrell, Evans M.
III.
Herd,
J.
V..
1937-
.
IV.
Series.
QA377.D63 1993
5
1
S.354~20
92-35875
CIP
Printed in the United
States
of America
92939495
EB
9
8
7
6
5 4 3 2 1
Contents
Preface
J. Asch and
P.
Duclos
An Elementary Model of Dynamical Tunneling
Jean Bellissard, Anton Bovier and Jean-Michel Ghez
Discrete Schrodinger Operators with Potentials
Generated by Substitutions
S.
De Bikvre,
J.
C. Houard and M. Irac-Astaud
Wave Packets Localized on Closed Classical Trajectories
R. M. Brown,
P.
D. Hislop and
A.
Martinez
Lower Bounds on Eigenfunctions and the
First Eigenvalue Gap
P.
J. Bushel1 and W. Okrasiriski
Nonlinear Volterra Integral Equations and The
Ap6ry Identities
Jean-Michel Combes
Connections Between Quantum Dynamics and
Spectral Properties of Time-Evolution Operators
W. E. Fitzgibbon and C.
B.
Martin
Quasilinear Reaction Diffusion Models
for
Exothermic Reaction
J. Fleckinger,
J.
Hernandez and
F.
de Thklin
A Maximum Principle for Linear Cooperative
Elliptic Systems
ix
1
13
25
33
51
59
69
79
V
vi
Con
tents
D. Fusco and
N.
Manganaro
Exact Solutions to Flows in Fluid Filled Elastic Tubes
87
F.
Gesztesy and
R.
Weikard
Spectral Deformations and Soliton Equations
101
G.
R.
Goldstein,
J.
A. Goldstein and Chien-an Lung
Nuclear Cusps, Magnetic Fields and the Lavrentiev
Phenomenon in Thomas-Fermi Theory
141
Bernard Helffer
On Schriidinger Equation in Large Dimension and
Connected Problems in Statistical Mechanics
153
Andreas M. Hinz
Regularity of Solutions for Singular Schrodinger Equations
167
Nail
H. Ibragimov
Linearization of Ordinary Differential Equations
Robert M. Kauffman
Expansion of Continuous Spectrum Operators in Terms
of Eigenprojections
Kazuhiro Kurata
On Unique Continuation Theorem for Uniformly
Elliptic Equations with Strongly Singular Potentials
S.
T.
Kuroda
Topics in the Spectral Methods in Numerical
Computation
-
Product Formulas
Elliott
H.
Lieb and Jan Philip Solovej
Atoms in the Magnetic Field of
a
Neutron Star
177
189
201
213
221
Con
tents
vii
C. McMillan and R. Triggiani
Algebraic Riccati Equations Arising in Game Theory
and in HW-Control Problems for
a
Class
of
Abstract Systems
M. C. Nucci
Symmetries and Symbolic Computation
L.
E.
Payne
On Stabilizing Ill-Posed Cauchy Problems for the
Navier-S tokes Equations
Robert
L.
Pego and Michael
1.
Weinstein
Evans’ Functions, Melnikov’s Integral, and
Solitary Wave Instabilities
James Serrin and Henghui Zou
Ground States
of
Degenerate Quasilinear Equations
Giorgio Talenti
Gradient Estimates, Rearrangements and Symmetries
Henry A. Warchall
Purely Nonlinear Norm Spectra and Multidimensional
Solitary Waves
Rudi Weikard
On Gelfand-Dickey Systems and Inelastic Solitons
Yuncheng You
Inertial Manifolds and Stabilization in Nonlinear Elastic
Systems with Structural Damping
239
249
261
2 73
287
307
313
325
335
347
Index
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Preface
Since the days
of
Newton, Leibniz, Euler and Laplace, mathematical
physics has been inseparably bound to differential equations. Phys-
ical and engineering problems continue to provide very important
models for mathematicians studying differential equations,
as
well
as
valuable intuition
as
to the solutions and properties. In recent
years, advances in computation and in nonlinear functional analysis
have brought rigorous theory closer to realistic applications, and
a
mathematical physicist must now be quite knowledgeable in these
areas.
In this volume we have selected several articles on the forefront
of research in differential equations and mathematical physics. We
have made an effort to ensure that the articles are readable
as
well
as
topical, and have been fortunate to include
as
contributions many
luminaries
of
the field
as
well as several young mathematicians doing
creative and important work. Some of the articles are closely tied
to work presented at the International Conference on Differential
Equations and Mathematical Physics,
a
large conference which the
editors organized in March,
1992,
with the support and sponsorship
of the National Science Foundation, the Institute for Mathematics
and its Applications, the Georgia Tech Foundation, and IMACS.
Other articles were submitted and selected later after
a
refereeing
process, to ensure coherence
of
this volume. The topics on which
this volume focuses are: nonlinear differential and integral equations,
semiclassical quantum mechanics, spectral and scattering theory, and
symmetry analysis.
These Editors believe that this volume comprises
a
useful chapter
in the life of our disciplines and we leave in the care
of
our readers
the final evaluation.
The high quality of the format of this volume is primarily due to
the efforts of Annette Rohrs. The Editors are very much indebted
to her.
W.
F.
Ames,
E.
M. Harrell
11,
J.
V.
Herod
Atlanta, Georgia, USA
ix