非線形解析とその応用

1995 Fiscal Year Annual Research Report

• Project/Area Number: 07454021
• Research Category: Grant-in-Aid for General Scientific Research (B)
• Research Institution: Chiba University
• Principal Investigator: 吉田 英信 千葉大学, 理学部, 教授 (60009280)
• Co-Investigator(Kenkyū-buntansha): 河原田 秀夫 千葉大学, 工学部, 教授 (90010793) ; 蔵野 正美 千葉大学, 教育学部, 教授 (70029487) ; 稲葉 尚志 千葉大学, 理学部, 教授 (40125901) ; 安田 正美 千葉大学, 理学部, 教授 (00041244) ; 高木 亮一 千葉大学, 理学部, 教授 (00015562)
• Keywords: 非線形解析 / 相分離現象 / 最適制御問題 / 横断ハウスドルフ次元 / パーコレーションモデル / デイリクレ問題 / ノイマン問題 / 超局所解析

Research Abstract

I.各分担者の専門の分野における非線形な現象について、いろいろなシンポジュウや研究集会等に出席した、全国の多くの研究者との討論等を通じて、これまでに為されてきた数々の研究についての情報を収集・整理した。それらを他分野の分担者と共に数度にわたって検討し、同一、類似のものに、整理、分類した。また、一同で、同一、類似の現象がどの分野においてどのように研究されてきたかを整理・検討した。この過程で、後に述べられるところの多くの研究成果が得られた。こうして、昨年度始めに計画された、初期の目的はほぼ達成されたと思う。
非線形の問題は、最近になってようやく研究され始めたばかりであり、我々の得た成果・情報は、非線形現象の多様さに比べて、微々たるものであることがこの共同研究を通じて痛感された。今回、他分野の分担者の助けと援助によって、各自の研究方法の上に、従来とは異なる視点が加えられ、個人の限界を打破する突破口とならんとしつつある。この研究を通して、共同で協力し助言しあった。単独では得られない新しい視点が得られ、改めて共同研究の大切さを実感させられた。
各大学、各研究機関において、私たちと同様な主旨で、非線形問題が扱われつつある。ぶんたん者の度々の出張によって、今年度も多くの役立つ情報が得られたが、更に、より広範な研究者からの助言とアドヴァイスが必要であることがわかってきた。次年度も継続して多くの情報をあつめ、得られた成果を公表して、今後の研究の進展に寄与したい。

Research Products

• [Publications] H.Yoshida: "A type of uniqueness for the Dirichlet problem on a half-space with continuous data," Pacific J.Math.(to appear).
• [Publications] H.Yoshida,I.Miyamoto,: "Solutions of the Dirichlet problem on a cone with continuous data" Journal of the Mathematical Society of Japan.
• [Publications] T.Inada and P.Walczak: "Transverse Hausdorff dimension of codim-1 C^2-foliations" Fundamenta Mathematicae. (to appear).
• [Publications] R.ISHIMURA: "The condition(s) of Kawai,the property of completely regular growth and the estimate of the micro-support of the complex of a convolution operator" Proceedings of the sixth intarnational colloguium on differential equations,Plovdiv,BULGARIA. (to appear).
• [Publications] R.ISHIMURA: "The micro-support of the complex defined by a convolution operator in tube domains" Proceedings of Banach Cantre Symposium on Singularities and Differential Equations,. 33. (1995)
• [Publications] Masami Kurano Youqiang Huang: "Average Reward Markov Decision Processes with Multiple Cost Constraints" Journal of Information & Optimization Sciences. Vol.16. 403-415 (1995)
• [Publications] Tanemura,H.: "Critical behavior for a continuum percolation model," Proc.Seventh Japan-Russia Svmp on Probability Theory,. (to appear). (1995)
• [Publications] Tanemura,H.: "A system of infinitely many mutually reflecting Brownian balls in R^d" Probabilty Theory and Related Fields.(to appear).
• [Publications] 汪 金芳・田栗正章: "ブートストラップ法-2標本問題からの考察" 統計数理. Vol.44(受理済). (1996)
• [Publications] Y.Okada,H.Yamane.: "Acharacteristic Cauduy problem in the comolex domain" J.Math.Pures et oppl.(to appear).
• [Publications] M.Nagisa: "Cocycle corjugacy of finary shifts on the hyperfinite factor of type II," Proc.Fourteenth. Symposium on Applied Functional Analyois. 123-127 (1995)
• [Publications] M.Nagisa: "Stable rank of some full group C^*-clgebas of groups oftalned by the free product" International Journal of Malteuiatics. (to appear).
• [Publications] M.Kurano,M.Yasuda,J.Nakagami,Y.Yoshida: "Markov-type fuzzy decision processes with a discounted reward on a closed interval," European Journal of Oprational Research,. (to appear).
• [Publications] M.Yasuda: "Explicit optimal value for Dynkin′s stopping Game," Mathl.Comput.Modelling,. Vol.22. 313-324 (1995)
• [Publications] J.Li,M.Yasuda,Q.Jiang,H.Suzuki,Z.Wang,G.J.KLir;: "Convergence of sequence of measurable functions of fuzzy measure space" Fuzzy Sets and Systems. (to appear).
• [Publications] Q.Jiang,H.Suzuki,Z.Wang,G.J.Klir,J.Li,M.Yasuda: "Property(p.g.p.)of Fuzzy Measures and Convergence in Measure," The Journal of Fuzzy Mathematics,. Vol.3. 669-710 (1995)
• [Publications] I.Miyamoto: "Harmonic functions in a cylinder which vanish on the boundary," Japanese J.Math.,. 1996 (22(2))
• [Publications] I.Miyamoto: "A type of uniqueness of solutions for the Dirichlet problem on a cylinder," Tohoku Math.J.(to appear).
• [Publications] H,Fujita,H.Kawahara,H.Kawarada.: "Distribution theoretic approach to fictitious domain method for Noumann problems" East-West J.Numer.Math. Vol.3. 111-126 (1995)
• [Publications] H.Kawarada.H.Koshigoe.A.Sasamoto.: "On Penctration phenomenon of magnetic ficld into superconducting mathcrials(Modcling and simulation)" Mathematical and Numcrial Aspects of Wavc propagation INRIA SIAM. 385-394 (1995)
• [Publications] H.Fujita,H.Kawarada A.Sasamoto: "Analytical and numerical approachcs to statinary fow problems with lesak and slip boundary conditions." Lecturc Notcs in Num.Appl.Anal.22GD21:14. 17-31 (1995)
• [Publications] B.Dacorogna H.Koshigoe.: "The quasiconvex cnvclope of the Saint Venant-Kirchhoff stored energy function in dimention 2" Analyse et Analyse numcrique. Nr.08.95. (1995)
• [Publications] T.Tsutsui: "Interaction of regular singularities in linear propagation" Kyuhu J.Math.49. 331-404 (1995)
• [Publications] N.Kenmochi M.Niezgodka: "Viscosity approach to modelling non-isothermal diffusive phase separation" Japan J.Industrial Appl.Math.Vol.13. 135-169 (1996)
• [Publications] N.Kenmochi.M.Niezgodka,I.Pawlow: "Subdifferential operator approach to the Cahn-Hilliard equation with constraint" J.Differential Equations. Vol.117. 320-356 (1995)
• [Publications] N.Kenmochi,M.Niezgodka S.Zheng: "Global attractor of a non-isothermal model for phase separation" Gakuto Intern.Ser.Math.Sci.Vol.5. 129-143 (1995)
• [Publications] N.Kenmochi: "Uniqueness of the solution to a nonlinear system arising in phase transition" Gakuto Intern.Ser.Math.Sci.Vol.7. 261-271 (1995)
• [Publications] J.Shirihzu,N.Sato N.Kenmochi: "Asymptotic convergence in models for phase change problems" Gakuto Intern.Ser.Math.Sci.Vol.7. 361-385 (1995)
• [Publications] Wang,J.and Taguri,M.: "Jackknifing:higher order accurate cenfidence intervals" Journal of the Japan Statistical Society. Vol.26(受理済). (1996)
• [Publications] Wang,J.,Ohuchi,S.and Taguri,M.: "Higher order accurate confidence internals for smooth funclions of means with application to the conelction coeffiend" Journal of Saiety of Computational Statistics. Vol.8(受理済). (1996)
• [Publications] R.Takagi,U-Hang Ki,T.Takahashi: "On some CR oubmanifolds uvith parallel mean curvature vector field in a umplex space form" Nihonkai Math.J.6. 215-226 (1995)
• [Publications] R Takagi Y-W.Choe H.S.Kim I-B.Kim: "Rigidity theorems fer real typersurfaces in a complex pojective space" Hokkaido Math.J. (to appear).
• [Publications] Y.Hino,S.Murakami: "Stability properties in abstract linear functional differential eguations with infinite deloy" WSSIAA(Dynamical sustoms and Applications. 329-341 (1995)
• [Publications] Y.Hino,S.Murakami: "Existence of an almoet periodic linear functional difforential equations with infinite clelay" Dynamical systems and applications. (to appear).