Table Of ContentNORTH-HOLLAND
MATHEMATICS STUDIES 81
Lecture Notes in Numerical and Applied Analysis Vol. 5
General Editors:
H. Fujita (University of Tokyo) and M. Yamaguti (Kyoto University)
Nonlinear Partial Differential
Equations in Applied Science;
Proceedings of The U.S.- Japan
Seminar, Tokyo, 1982
Edited by
HlROSHl FUJITA (University of Tokyo)
PETER D. LAX (New York University)
GILBERT STRANG (Massachusetts Institute of Technology)
1983
NORTH-HOLLAND PUBLISHING COMPANY
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@ 1983 by Publishing Committee of Lecture Notes in Numerical and Applied Analysis
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Distributed in Japan by KINOKUNIYA COMPANY LTD.
Lecture Notes in Numerical and Applied Analysis Vol. 5
General Editors
H. Fujita M. Yamaguti
University of Tokyo Kyoto Universtiy
Editional Board
H. Fujii, Kyoto Sangyo Universtiy
M. Mimura, Hiroshima University
T. Miyoshi, Kumamoto University
M. Mori, The University of Tsukuba
T. Nishida, Kyoto Universtiy
T. Nishida. Kyoto University
T. Taguti, Konan Universtiy
S. Ukai, Osaka City Universtiy
T. Ushijima, The Universtiy of Electro-Communications
PRINTED IN JAPAN
P R E F A C E
Nonlinear equations come to us in tremendous variety, each with its own
questions and its own difficulties. At one extreme are the completely integrable
equations, with constants of the motion and a rich algebraic structure. At the
other extreme is chaos, with turbulent solutions and statistical averages.
Between these two possibilities, algebraic and ergodic, lies the full range of
nonlinear phenomena. There are smooth solutions which develop shocks, or
bifurcate, or maintain slow and nearly periodic variations that imitate the linear
theory. Each of these questions requires a separate treatment, and the subject
would be simpler if we know for every equation which behavior to expect.
Nevertheless these equations, the nonlinear partial differential equations
which arise in applications, share one crucial property. They are all vulnerable
when the right pattern in found. It is a slow process, to uncover and reveal their
structure, but it is moving forward.
The papers in this volume reflect a part of that progress. They were
presented at the U.S.-Japan Seminar in Tokyo in July 1982.
One goal of the seminar was to establish personal contact among those
mathematicians who are actively working for these difficult but fascinating
equations in the U.S. and in Japan. The other goal was a wider one, that is, to
invoke most advanced scientific talks and discussions on major topics in this
developing field of applied analysis.
Thanks to the cooperation of all participants from the U.S., Japan, and
some third countries including China, the seminar was successful in both sense
mentioned above and we believe that these proceedings of the seminar which
contain all papers delivered there will contribute much to the progress of the
study of nonlinear problems.
Finally, we, who served also as the coordinators of the seminar, wish to
express our gratitude to the governmental agencies, i.e., National Science
Foundation and Japan Society for the Promotion of Science, for their support
and to industrial companies in Japan for practical assistances which they gave as
institutional participants. Last but not least, our gratitudes go to all of our
committee members and staff members of the secretariat of the seminar for their
enthusiasm and devotion.
September 15, 1983
H. FUJITA
P. D. LAX
G. STRANG
P R O G R A M
MONDAY, JULY 5
8:45 Opening of Seminar
Session 5-1
9:OO-1O:OO Prof. T. Kato (University of California, Berkeley)
“Quasi-Linear Equations of Evolution in Nonreflexive Banach Spaces”
10:15-11:OO Prof. K. Masuda (T6hoku University)
“Some Remarks on Blow-up of Solutions of Nonlinear Diffusion
Equations”
11:05-11:50 Dr. T. Suzuki (University of Tokyo)
“Deformation Formulas and their Applications to Spectral and Evolu-
tional Inverse Problems”
Session 5-2
13:45-14:30 Mr. H. Okamoto (University of Tokyo)
“Stationary Free Boundary Problems for Circular Flows with or without
Surface Tension”
14:35-15:20 Prof. Lin Qun (Institute of Systems Science, Academia Si-
nica) and Prof. Jiang Li-shang (Peking University)
“The Existence and the Finite Element Approximation for the System
15:20-16:OO Coffee Break
16:OO-17:OO Prof. H. F. Weinberger (University of Minnesota)
“A Simple System with a Continuum of Stable Inhomogeneous Steady
States”
TUESDAY, JULY 6
Session 6-1
9:OO-1O:OO Prof. R. J. DiPerna (Duke University)
“Shock Waves and Entropy”
10:15-11:OO Prof. S. Ukai (Osaka City University) and Prof. K. Asano
(Kyoto University)
“Stationary Solutions of the Boltzmann Equation”
11:05-1150 Prof. T. Nishida (Kyoto University) and Dr. A. Matsumura
(Kyoto University)
“Initial Boundary Value Problems for the Equations of Compressible
Viscous and Heat-Conductive Fluid”
Session 6-2
X Program
13:45-14:30 Prof. S. Miyatake (Kyoto University)
“Integral Representation of Solutions for Equations of Mixed Type in a
Half Space”
14:35-15:20 Prof. H. Fujii (Kyoto Sangyo University) and Prof. Y.
Nishiura (Kyoto Sangyo University)
“Global Aspects in Bifurcation Problems for Nonlinear Diffusion Sys-
tems” (tentative)
15:20-16:OO Coffee Break
16:OO-17:OO Prof. A. C. Newell (University of Arizona)
“Two-Dimensional Convection Patterns in Large Aspect Ratio Sys-
tems”
WEDNESDAY, JULY 7
Session 7-1
9:OO-1O:OO Prof. M. Sat0 (Research Institute for Mathematical Sciences,
Kyoto University)
“Soliton Equations as Dynamical Systems on Infinite Dimensional
Grassmann Manifold”
10: 15-1 1:00 Prof. A. C. Newell (University of Arizona)
“The Connection between Wahlquist-Estabrook, Hirota, r Function, and
Inverse Scattering Methods for the AKNS Hierarchy”
11:05-1150 Prof. Zhou Yu-lin (Peking University)
“Some Problems for Nonlinear Evolutional Systems of Partial Differen-
tial Equations”
THURSDAY, JULY 8
Session 8-1
9:OO-1O:OO Prof. M. Yamaguti (Kyoto University)
“‘Chaos’ Caused by Discretization”
10: 15-1 1:OO Prof. H. Matano (Hiroshima University)
“Asymptotic Behavior of the Free Boundaries Arising in One Phase
Stefan Problems in Multi-Dimensional Spaces”
11:05-1150 Dr. E. Hanzawa (Hokkaido University)
“Nash’s Implicit Function Theorem and the Stefan Problem”
Session 8-2
13:45-14:30 Prof. H. Kawarada (University of Tokyo)
“New Penalty Method and its Application to Free Boundary Problems”
14:35-15:20 Prof. T. Ushijima (University of Electro-Communications)
“On the Linear Stability Analysis of Magnetohydrodynamic System”
15:20-16:00 Coffee Break
16:OO-17:OO Prof. G. Papanicolaou (Courant Institute of Mathematical
Sciences, New York University)
Program xi
“Modulation Theory for the Cubic Schrodinger Equation in Random
Media”
FRIDAY, JULY 9
Session 9-1
9:OO-1O:OO Prof. R. V. Kohn (Courant Institute of Mathematical Science,
New York University)
“Partial Regularity for the Navier-Stokes Equations”
10:15-11:OO Mr. Y. Giga (Nagoya University)
“The Navier-Stokes Initial Value Problem in Lp and Related Problems”
11:05-1150 Prof. J. G. Heywood (University of British Columbia)
“Stability, Regularity and Numerical Analysis of the Nonstationary
Navier-Stokes Problem”
Session 9-2
13:45-14:30 Prof. Ying Lung-an (Peking University) and Prof. Teng
Zhen-huan (Peking University)
“A Hyperbolic Model of Combustion”
14:35-15:20 Prof. T. Miyoshi (Kumamoto University)
“Yielding and Unloading in Semi-Discrete Problem of Plasticity”
15:20-16:OO Coffee Break
16:OO-17:OO Prof. G. Strang (Massachusetts Institute of Technology)
“Optimization Problems for Partial Differential Equations”
17:05 Closing of Seminar
DIRECTORY OF PARTICIPANTS
OF
US-JAPAN SEMINAR '82 IN APPLIED ANALYSIS
GUESTS OF SEMINAR
Professor Tetsuichi Asaka
Science University of Tokyo
(Emeritus Professor of University of Tokyo)
Dr. Tatuo Simizu
Laboratory of Shimizu Construction Co. Ltd.
Professor Shoji Tanaka
University of Tokyo
Dr. Hajimu Yoneguchi
Nippon UNIVAC Sogd Kenkyusho, Inc.
FOREIGN PARTICIPANTS
(US Delegates)
Ronald J. DiPerna Duke University
Tosio Kato University of California, Berkeley
Robert V. Kohn Courant Institute of Mathematical
Sciences, New York University
Alan C. Newell The University of Arizona
George Papanicolaou Courant Institute of Mathematical
Sciences, New York University
Gilbert Strang Massachusetts Institute of Technology
Hans F. Weinberger University of Minnesota
(Special Participants from Third Countries)
John G. Heywood The University of British Columbia
Lin Qun Institute of Systems Science,
Academia Sinica
Ying Lung-an Peking University
Zhou Yu-lin Peking University
xiv Directory of Participants
JAPANESE PARTICIPANTS
Rentaro Agemi Hokkaido University
Kiyoshi Asano Kyoto University
Hiroshi Fujii Kyoto Sangyo University
Hiroshi Fujita University of Tokyo
Daisuke Fujiwara Tokyo Institute of Technology
Isamu Fukuda Kokushikan University
Yoshikazu Giga Nagoya University
Ei-Ichi Hanzawa Hokkaido University
Masayoshi Hata Kyoto University
Imsik Hong Nihon University
Yuzo Hosono Kyoto Sangyo University
Atsushi Inoue Tokyo Institute of Technology
Hitoshi Ishii Chuo University
Nobutoshi Itaya Kobe University of Commerce
Masayuki Ito Hiroshima University
SeizB It6 University of Tokyo
Tatsuo Itoh University of Tokyo
Takao Kakita Waseda University
Hideo Kawarada University of Tokyo
Shuichi Kawashima Nara Women’s University
Fumio Kikuchi University of Tokyo
Hikosaburo Komatsu University of Tokyo
Yukio K6mura Ochanomizu University
Yoshio Konishi University of Tokyo
Takeshi Kotake Tohoku University
ShigeToshi Kuroda University of Tokyo
Kyoya Masuda Tohoku University
Hiroshi Matano Hiroshima University
Akitaka Matsumura Kyoto University
Akihiko Miyachi University of Tokyo
Isao Miyadera Waseda University
Sadao Miyatake Kyoto University
Tetsuhiko Miyoshi Kumamoto University
Sigeru Mizohata Kyoto University
Ryuichi Mizumachi Tohoku University
Hiroko Morimoto Meiji University
Directory of Participants xv
Katsuya Nakashima Waseda University
Yoshimoto Nakata Science University of Tokyo
Takaaki Nishida Kyoto University
Yasumasa Nishiura Kyoto Sangyo University
Hisashi Okamoto University of Tokyo
Shin Ozawa University of Tokyo
Mikio Sat0 Kyoto University
Yasuko Sat0 Ryukyu University
Norio Shimakura Kyoto University
Taira Shirota Hokkaido University
Takashi Suzuki University of Tokyo
Masahisa Tabata The University of Electro-Communications
lzumi Takagi Tokyo Metropolitan College of
Aeronautical Engineering
Hiroki Tanabe Osaka University
Seiji Ukai Osaka City University
Teruo Ushijima The University of Electro-Communications
Shigehiro Ushiki Kyoto University
Masaya Yamaguti Kyoto University
Kiyoshi Yoshida Kumamoto University
KGsaku Yosida University of Tokyo
xvi Directory of Participants
INSTITUTIONAL PARTICIPANTS
AISl 4 SE Co., Ltd.
AISIN-WARNER Ltd.
B UN-EIDO
Energy Research Laboratry, Hitachi, Ltd.
FACOM HITAC
FUJIFACOM CO.
Fujitsu Ltd.
FUKUMOTO-SHOIN, Ltd.
Hitachi Ltd., Central Research Laboratory
Hitachi Ltd., Software Works
Hitachi Ltd., System Development Laboratory
Hitachi Software Engineering Co., Ltd.
HOKUSHIN ELECTRIC WORKS Ltd.
IBM Japan, Ltd.
Institute of Japanese Union of Scientists and Engineers
Ishikawajima-Harima Heavy Industries Co., Ltd.
Japan Advanced Numerical Analysis. Inc.
Japan Process Development Co., Ltd.
Japanese Standards Association
Kajima Co.
Kawasaki Steel Co., Chiba Works
KENBUN SHOIN Co., Ltd.
Kyoei Information Processing Service Center Ltd.
Maeda Construction Co., Ltd.
Mitsubishi Central Research Laboratory
Mitsubishi Heavy Industries Co., Ltd.
Mitsubishi Research Institute Inc.
N.C.R. Japan Ltd.
NIPPON BUSINESS CONSULTANT Co., Ltd.
Nippon Electric Company (C & C Systems Research Laboratories)
Nippon Sheet Glass Co.
Nippon UNIVAC Kaisha, Ltd.
Oki Electric Industry Company, Ltd.
PANAFACOM Ltd.
Shimizu Construction Co., Ltd.
Surugadai Gakuen
