2006 Fiscal Year Final Research Report Summary
Study on the nonlinear phenomena with moving boundaries
| Project/Area Number |
16540184
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Hitotsubashi University |
|---|
Principal Investigator |
ISHIMURA Naoyuki Hitotsubashi University, Graduate School of Enocomics, Professor, 大学院経済学研究科, 教授 (80212934)
|
|---|
| Project Period (FY) |
2004 – 2006
|
| Keywords | phase separation / nonlinear PDE / EOM system / Mathematical Finance / transaction costs |
|---|
| Research Abstract |
This research project is mainly concerned with the next two subjects, among the popular research topics of nonlinear phenomena involving the moving boundaries. 1 : Study on the phase separation. 2 : Study on the exercise boundary in mathematical finances.
1.The author has been tackling the analysis of a model equation proposed by Professor T.Eguchi, which describes the phase separation in terms of two unknown variables. One is the local concentration and the other is the local degree of order. The model consists of coupled two evolution equations ; one is 4^<th> order and hence the analysis is tough. We concentrate on the one-dimensional case and we obtain fairy a lot of results. The first one is one the existence of solutions and the structure of steady state solutions. Analysis of a singular perturbation problem and a bifurcation problem then follows. We publish these papers in various journal, which are rather well estimated by anonymous referees.
2.The author gives a set of exact solutions for the model equation proposed by K.Takaoka, which extends the famous Black-Scholes analysis. Then the author tries to solve the partial differential equations with the effect of transaction costs. The paper is submitted now.
The research of the phase separation still continues. The direction with respect to the dynamical system seems promising and the work is now in progress.
|
