2007 Fiscal Year Final Research Report Summary
Study on Navier-Stokes equations and the related nonlinear differential equations
| Project/Area Number |
18540222
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Meiji University |
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Principal Investigator |
MASUDA Kyuya Meiji University, Department of Mathematics, Professor (10090523)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIMURA Naoyuki Hitotsubashi University, Department of Economics, Professor (80212934)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Probabilistic Control Problem / Optimal Investment Problem / Phase transiton in binary alloys / Mahemtical Economics / Mathematical Pysics |
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| Research Abstract |
In the period 2006-2007, Masuda studied the dynamical behavior in time of solution of a model describing the phase transition in binary in alloys. This model is described by a system of partial differential equations of the forth order, proposed by Eguchi-Oki-Matsumura(1984).
Masuda succeeded in showing the existence of maximal attractor and inertial set for the so-called Eguch-Oki-Matsumra Equation and reported the results in the International Congress held at Athens.
The Hoggard-Whalley-Willmott equation is introduced to mode portforios of European type options incorporating transaction costs. The model gives rise to a nonlinear parabolic partial differential equation, whose nonlinearity reflects the presence of transaction costs. Ishimura showed analytically the existence of solutions which are deviced to effectively handle an infinite domain and unbounded solution.
Also Ishimura deal with numerical computation of solution. Numerical computation shows the validity of the scheme proposed by Ishimura.
Ishimura is concerned with the solvability of certain partial differential equations, which is derived from the optimal Investment problem under the random risk process. The equations describe the evolution of the Arrow-Pratt coefficient of absolute risk aversion woth respect to the optimal value function.
Employing the fixed point approach combined with the convergence argument Ishimura shows the existence of solution.
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Research Products
(10 results)
