1998 Fiscal Year Final Research Report Summary
Resarchs on Solutions of Nonlinear Elliptic Equations and Numcrical Analysis
| Project/Area Number |
09440087
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Ryukoku University |
|---|
Principal Investigator |
YOTSUTANI Shoji Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (60128361)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YANAGIDA Eiji Grad.School of Math.Sciences, Univ.of Tokyo, Assoc.Prof., 数理科学研究科, 助教授 (80174548)
YAMADA Yoshio Faculty of Science & Technology, Waseda Univ., Professor, 理工学部, 教授 (20111825)
OKA Hiroe Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (20215221)
MORITA Yoshihisa Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (10192783)
IKEDA Tsutomu Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (50151296)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | elliptic equation / Poisson's equation / charge simulation method / radially symmetric / reaction-diffusion / standing pilse / cross-diffusion / Ginzburg-Landau equation |
|---|
| Research Abstract |
Head investigator S.Yotsutani proposed a very accurate numerical computation method to solve Poisson's equation by using a charge simulation method with H.Morishita, N.Kobayashi, H.Takaichi and K.Amano. Recently, He has succeeded to shorten the time of the calculation considerably and improve the accuracy with H.Morishita and K.Anjano, This method is in the conformity with the paerallel computing. Thus it is possible to know the detailed shape of solutions of nonlinear elliptic systems.
On the other hand, he developed the mathematical method of investigate the shape of radially symmetric solutions with Y.Kabeya and E.Yanagida. Recently, he has found the systematic change of variables to transform the differential equations arising from the elliptic equations to canonical form with E.Yanagida. Thus, relations between various equations studied one by one independently become very clear, and the understandings encourage the deep understanding of the propertites of each solution.
The reserach results of investigators are asfollows. T.lkeda invesitigate the instabiliz ation of the standing pulse solutions of bistable reaction-diffusion systems. Y.Morita showed stabilization of vorticies in the Ginzburg-Landau equation with a variable diffusion coefficient. H.Oka investigated the connecting orbit structure of monotone solutions in the shadow system. Y.Yamada proved the coexistence states for some population models with nonlinear cross-diffusion. E.Yanagida discoverd various new phenomena of the systems of parabolic equations and gave the proof of them.
|
