数理解析研究所講究録 755

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数理解析研究所講究録 755

発展方程式と

非線型問題への応用

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京都大学数理解析研究所

1991 年 6 月

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R:MS Ko hyu,teo leLc 755

Evo1ution to

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Nonlinear

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Research Znstitute for Mathematical Sciences

Kyoto University, Kyoto, Japan

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Preface

This volume is the proceedings of the conference on ”Evolution Equations and

Applications to Nonlinear Problems”, held iR Kyoto University, RIMS, during October 24 - 26, 1990.

This series of conferences on evolution equations and related topics was al- ready organized by:

e S. Oharu (Hiroshima University), 1983;

e S. Ohaiu (Hiroshima University), 1984;

e H. Tanabe (Osaka University), 1985;

. e H. Tanabe (Osaka University), 1986s e Y. K6mura (Ochanomizu University), 1987;

e Y. K6mura (Och&nomizu University), 1988;

)

e N. Kenmochi (Chiba University), 1989;

e N. Kenmochi (Chiba University), 1990;

and it has been supported by many other mathematicians. Every meeting was very successfu1 in respect that new orientations of research in this field were in- dicated, various liRear or nonlinear theory on evolution equations were evolved and their applications to real problems were discussed. Also, it should be noted that many young mathematicians were invited to every meeting as main speakers; this seems quite important for new development of research in our future;

the organizers are satisfactory enough in this point.

Finally the organizer of 1990 vvishes to express his thanks to all speakers and all participants for their contributions to the meeting.

Organizer of the 8tb meeting

N. Kenmochi April 25, 1991

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発展方程式と非線型問題への応用研究集会1990年10.月24日一26日研究代表者:剣持信幸(Nobuyuki Kenmochi)

1. An Estimate on the Rate of Convergence of Viscosity Solutions for the Singular Perturbation Problems一一一一一一一一一一一一一一一一

神戸大・自然科学石井克幸(K:atsuyuki ls:h五) 神戸大・理山田直記(Nao:ki Yamada)

2・Comparison P血Ciple and Convexity P reserving Properties for SingUlar Degenerate Parabolic Equations on Unbounded Domains一一一一一一一一一一

北大・理儀我美一(Yoshikazu Giga)

・北大・理後藤俊一(Shun,ichi Goto) 中央大・理工石井仁司(Hitosbi IS】血) 北大・理佐藤元彦(Moto一:hiko Sato) 3. Existence of Positive Entire Solutions for Semvanear Eurptic

Systems一一一一一一一一一一一一一一一.一一一一..一.一.一一一.一.

佐賀大・理工古庄康浩(Yasuhiro liUru8ho)

4. On Positive S olutions of Singular Emden-Fowler Type Eequations一一一一一一一広島大総合科宇佐美広介(Hiroyuki Usami)

5. Approximation of ln ertial Manifolds for Semilinear Evolution Equations 湘南大・工小林和夫(Kazuo Kobayasi)

6. Convergence Theorems for the Pseudo-Conformally lnvariant

Nonlinear Schr6dinger Equation一一一一一一一一一一一一一一一一一一一束工大・理名和範人(Hayato N&wa)

b1

10

28

48

61

73

7. Schr6dinger Evolution Equations and Associated Smoothing Effect一一一一一一一93 東大・教養谷島賢二(Kenji Yajima)

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8.A Mathematical Model for Non tSothermal Crysta皿iZation一一一 Univ. Firenze

Uniy. Firenze U皿i▼.Fire皿ze

D. Andreucci

A.Easa皿o

M. Primicerio

一一一一一112

9. lilee Boundary P roblems lnvolving Non-Local Components一一一一一一一一一121 千葉大・教育剣持信幸(Nobuyuki Kenmochi)

Warsaw Univ. M. Niezg6dka

10e A Parabolic lnverse P roblem in Chromat ography一一一一一一一一一一一一一127 花王文理科学研木村毅(Tuyoshi Kim皿m)

都立大・理鈴木貴(Takashi Suzuki)

11. Semigroups of Loca lly Lipschitzian Operators一一一一一一一一一一一一一一一134 新潟大・工小林良和(Yoshikazu:K obayashi)

広島大・理堅甲慎之助(Shinnosuke Oharu)

12・Li皿ear E▼olution Equations in a Refle:Xi▼e Banach Space。一。一。一一156 早大・理工田中直樹 (Naoki Tana:la)

13.界面における化学反応のモデルー解の漸近挙動について一一一一一一・一171 阪大・理飯田雅人 (Masato ma)

早大・理工山田義雄(Yoshio Yamada) 龍大・連工四ツ谷晶二

(Shoji Yotsutani)

14, Shape Optimization in Multi-Phase Stefan Problem一一一一一一一一 185 千葉大・自然科学角谷敦(At sushi K adoya)