IssN 1880-2818

数理解析研究所講究録 1542

現象の数理モデルと発展方程式

京都大学数理解析研究所

2007 年 4 月

RIMS Kk5kyOroku Z542

Mathematical Models ofPhenomenaand Evolution Equations

AprzL 2007

Research institute for Mathematical Skeienees
Kvoto Uhtversity, K)2oto, ,lapan
This is a report of research done at Research Institute fbr Mathemactcal

Sciences, Kyoto University The papers contamed herem are m final form
and will not be submitted for publication elsewherePreface

This volume collects the papers based on the lectures delivered at theconference Mathematzcal Models of Phenomena and Evolutzon Equatzons,
held at Research Institute for Mathematical Sciences, Kyoto University(Kyoto, Japan), durmg the penod October 18-20, 2006. The main ob-

jective of the conference was modelmg of various phenomena by meansof evolution equations and the development of the theory to describe themodels from the view pomt of evolution equations
It is my great pleasure to thank all those who contnbuted their papers
to this volume and all the participants of the conference.
Naoki Yamada
Fukuoka UniversityFebruary 14, 2007

現象の数理モデルと発展方程式

Mathematical Models of Phenomena and Evolution Equations
RIMS 研究集会報告集
˜
2006 年 10 月 18 日{}10月 20 日研究代表者 山田 直記 (Naoki Yamada)目次

1 氷の内部融解・凍結による六角板状の真空泡形成のモデリングに向けて
Towards modellmg the formation of negative ice crystals or vaper figures
prOduced by freemng of mterna1 melt figure s 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・一・・・・…の一・…e1
岐阜大・教育 (G 血 U) 石渡 哲哉 (Tetsuya Ishlwata)
宮崎大・工 (UMlyazak1) 矢崎 成俊 (Shlgetosh1 Yazak1)
2AN APPLICATION OF AUBRY.MAT 朋 R THEORY IN
LOREN TZIAN GEOMETRY ・…d・一一一…一一一一一一一一一一一一一一一一一・・一 b 一一一一一一一一一一一一一一一一一一一・一一一一一一一一一一一一…一一一一一一 12

Univ di Roma

La Sapienza

Antomo S iconolfi

3 Asymptotic solutions of Hamilton-Jacobi equations with non-penodic penurbations 一一一一一 24
阪大・基礎工学 (Osaka U) 市原 直幸 (Naoyuki lchlhara)
4 Asymptotic solutions of Hamilton-Jacobi equations with state constramts 一一一一一一一一一一一一一一 33
早大・理工学 (Waseda U) 三竹 大寿 (Hlroyoshl Mltake)
5 A Lotka-Volterra Cross-Diffusion Model m Spatially Heterogeneous Environments 一一一一一 41
福岡工業大・工 (Fukmoka Inst of Tech) 久藤 衡介 (KousUke Kuto)

6 Existence and Nonexistence of the Global S olutions
fOr a ReaCtlon-DlffilSIOn System 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 t 一 58
北大・理学 (Hokkaldo U) 山内 雄介 (Yusuke Yamauch 1)
7 Smgular pe 血 rbation problem for nonlmear・diffuslve loglstic equatlons 一一一一一一…一。・・一一一・一 77

工学院大・工 (Kogakum U) 竹内 慎吾 (Shmgo Takeuch1)

8 . On positivity of solutions of semi-lmear convection-diffusion-reaction systems,with applications m ecology and environmenta1 engmeenng 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 92

Technische Umv Munchen Messoud A. Efendiev
Univ of Guelph Hermann J. Eberl

9 Convergence of Qptrmal Control for Quasihnear Elliptic-Parabolic Vanational
InequalMes with Time-Dependent Constramts 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 102
室蘭工大 (Muroran・lnst of Tech) 山崎 教昭 (Nonaki Yamazaki)
1 O , Free boundary prob lem for elastic matenal with 1inear stram 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 1171112

岐阜大・教育 (Glfu U) 愛木 豊彦 (Toyohlko Aiki)
The uniqueness and existence of level sets for motion of spirals 一一一一一一一一一一一一一一一一一一一一一一一一一一 123
東大・数理科学 (Uof Tokyo) 大塚 岳 (Takeshi Ohtsuka)

THE EXISTENCE OF MULTIPLE SOLUTIONS FOR NONLINEARI.Y
PERTURBED PARABOLIC-ELLIPTIC S YSTEM S OF KELLER-SEGEL
TYPE IN R2 一一一 e.. 一.. 一一.. 一.. 一 eDee 一一 eeeeee) 一一一 be 一一一一 e. 一一一一一一一 .. 一一一一. 一一 e.e 一一一一 一 eeenee 一一 e 一一一 ts 一.... 一. 一一. 136

13

東北大・理学 (Tohoku U) 石渡 通徳 (Mlchmon Ishlwata)Large time behavior of bounded solutions to a parabolic system of chemotaxis
m the whole space 一一 e 一一一 e. 一一 .n.... 一 m 一一一一一. . 一. 一 e 一一一一一 e eee.ebeee 一一一.n 一 一

ee 一一 eeeee . 一 . 145

広島大・理学 (Hlroshlma U) 山田 哲也 (TetSuya Yamada)