Nonlinear Partial Differential Equations in Applied Science; Proceedings of The U.S.-Japan Seminar, Tokyo, 1982 PDF
Preview Nonlinear Partial Differential Equations in Applied Science; Proceedings of The U.S.-Japan Seminar, Tokyo, 1982
NORTH-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 AMSTERDAM NEW YORK. OXFORD KINOKUNIYA COMPANY LTD. TOKYO JAPAN NORTH-HOLLAND PUBLISHING COMPANY -AMSTERDAM,NEW YORK,OXFORD KINOKUNIYA COMPANY -TOKYO @ 1983 by Publishing Committee of Lecture Notes in Numerical and Applied Analysis All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN: 0 444 86681 7 Publishers NORTH-HOLLAND PUBLISHING COMPANY AMSTERDAM-OXFORD-NEW YORK * * * KINOKUNIYA COMPANY LTD. TOKYO JAPAN Sole distributors for rhe U.S.A; and Canada ELSEVIER SCIENCE PUBLISHING COMPANY. INC. 52 VANDERBI1.T AVENUE NEW YORK. N.Y. 10017 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
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