Investigation of Inverse Problems for the Heat equation Based on the Theory of Stochastic Control
| Project/Area Number |
16540100
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kanazawa University |
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Principal Investigator |
TSUCHIYA Masaaki Kanazawa Univ., Grad.School of Nat.Sci.Tech., Prof., 自然科学研究科, 教授 (50016101)
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| Co-Investigator(Kenkyū-buntansha) |
FUJISAKI Masatoshi Univ.Hyogo, School of Business Administration, Prof., 経営学部, 教授 (20047492)
KANJIN Yuichi Kanazawa Univ., Grad.School of Nat.Sci.Tech., Prof., 自然科学研究科, 教授 (50091674)
KAWAKAMI Hajime Akita Univ., Fac.of Engi.Rsource Sci., Asso.Prof., 工学資源学部, 助教授 (20240781)
FUJISAKI Hiroshi Kanazawa Univ., Grad.School of Nat.Sci.Tech., Lecturer, 自然科学研究科, 講師 (80304757)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | heat equation / inverse problem / stochastic control / jump process / Jacobi series / Cesaro operator / spectral spreading sequence / discretized Markov transform / 超離散力学系 / 時系列モデル / マルコフ連鎖 |
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| Research Abstract |
We study the inverse problem determining the shape of some unknown portion of the boundary of a domain based on parabolic equations and also study the one determining the heat conduction coefficients of a heat equation based on the theory of stochastic control. The former is treated through a suitably linearized equation by analytical method. The shape of deforming unknown portion is allowed depending on time and is assumed only to be Lipschitz continuous. The latter provides us with a new type of stochastic control. That is, the running cost is driven by the local time at the measurement place with respect to the controlled diffusion process. Therefore the corresponding HJB equation has singular source term involving the Dirac function supported on the measurement place.
In the framework of stochastic control, we also consider some jump process concerned with common property resource and obtain an optimal control variable under suitable conditions.
Related to the subject, we need to study some property of systems of orthogonal functions. In particular, the classical Hardy's inequality is extended to the case of Jacobi series and the boundedness of the transplantation operators and Cesaro operators are obtained.
Finally, from a viewpoint of numerical analysis, we study some random sequences. An ultradiscrete dynamical system is constructed under consideration of discretized Markov transforms and bit error probabilities of certain communication systems are discussed by using spreading sequences of Markov chains.
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Report
(3 results)
Research Products
(27 results)
