1998 Fiscal Year Final Research Report Summary
Studies on linear and nonlinear differential equations with time delay
| Project/Area Number |
09640184
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| 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)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
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)
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)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | Differential Integral Equation / Mittag-Leffler function / Muskat Problem / Interface / Free Boundary Problem |
|---|
| Research Abstract |
The differential-integral equation with time lag, Chen's equation, was studied by constructing the fundamental solutions using Puiseux and Laplace expansions. Also, long-time behavior of the equation was determined in detail by the asymptotic series characterized by the Mittag-Leffler function. Chen's equation originally describes the motion of a spherical particle in fluid have a close connection with the equations of dynamics of 2-species 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 weak-limit 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.
|
