2014 Fiscal Year Final Research Report
Singular perturbation problems for viscous Hamilton-Jacobi equations
| Project/Area Number |
24740089
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Aoyama Gakuin University (2014)
Hiroshima University (2012-2013) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 確率最適制御 |
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| Outline of Final Research Achievements |
In this research, we studied viscous Hamilton-Jacobi equations, a class of nonlinear partial differential equations, and associated stochastic optimal control problems. More specifically, for a family of viscous Hamilton-Jacobi equations with real parameter, we showed that the asymptotic behavior, at infinity, of solutions changes drastically in the vicinity of a certain critical point of parameter. Furthermore, we also proved that the recurrence/transience of the optimal trajectory for the associated stochastic optimal control problem also changes at this critical point, and that this phenomenon relies heavily on the choice of nonlinearity in gradient of the equation.
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| Free Research Field |
確率論
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