Project/Area Number  09640184 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Osaka University 
Principal Investigator 
KAMETAKA Yoshinori Osaka University, Graduate School of Engineering Science, Professor, 大学院・基礎工学研究科, 教授 (00047218)

CoInvestigator(Kenkyūbuntansha) 
久保 雅義 大阪大学, 大学院・基礎工学研究科, 助手 (10273616)
亀山 敦 大阪大学, 大学院・基礎工学研究科, 助手 (00243189)
OGAWA Toshiyuki Osaka University, Graduate School of Engineering Science, . Associate Professor, 大学院・基礎工学研究科, 助教授 (80211811)
NAGAI Hideo Osaka University, Graduate School of Engineering Science, Professor, 大学院・基礎工学研究科, 教授 (70110848)
FUKUSHIMA Masatoshi Kansai University, Faculty of Engineering, Professor, 工学部, 教授 (90015503)
MOCHIZUKI Kiyoshi Tokyo Metropolitan University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80026773)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Differential Integral Equation / MittagLeffler function / Muskat Problem / Interface / Free Boundary Problem / マスカット問題 / 自由境界問題 / 非線形放物形偏微分方程式 / 自由境参問題 / 非線形放線形偏微分方程式 / 微分積分方程式 / ミッタークレフラ関数 / 境界層 
Research Abstract 
The differentialintegral equation with time lag, Chen's equation, was studied by constructing the fundamental solutions using Puiseux and Laplace expansions. Also, longtime behavior of the equation was determined in detail by the asymptotic series characterized by the MittagLeffler function. Chen's equation originally describes the motion of a spherical particle in fluid have a close connection with the equations of dynamics of 2species fluids mixture. Professor Radkevich in Moscow University had been staying at our department for four and half months through March 1998. The Muskat problem, nonlinear elliptic partial differential equation describing the interfacial motion between oil and water, has been studied jointly with him. The joint work is still going on. Our main idea is to characterize the weak solution to the Muskat problem as the weaklimit of the smooth solution of the nonlinear parabolic partial differential equation which has the small parameter corresponding the width of the interface. This idea is actually true for the case of the symmetric domain as a ball. These results will appear in the journal, Applicable Analysis. 結果は共著論文として発表予定である。
