2017 Fiscal Year Final Research Report
Dynamical structure on degenerate Hamilton-Jacobi equations
| Project/Area Number |
15K17574
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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 |
Mathematical analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Research Collaborator |
GIGA Yoshikazu
GOMES Diogo A.
ISHII Hitoshi
SICONOLFI Antonio
SOGA Kohei
TRAN Hung V.
YAMADA Naoki
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 粘性解理論 / 弱KAM理論 / 退化粘性ハミルトン・ヤコビ方程式 / 生成伝播型微分方程式 / 非線形随伴法 / ディスカウント近似 |
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| Outline of Final Research Achievements |
The main purpose of this project is to develop a qualitative analysis of degenerate Hamilton-Jacobi (HJ) equations and weakly coupled systems in the spirit of weak KAM theory. More precisely, I focused on a selection problem in the vanishing discount process for degenerate HJ equations with convex Hamiltonians and proved the convergence of approximated solutions by using the nonlinear adjoint method. Also, I started to work on nonconvex HJ equations and rate of convergence on the vanishing discount problem, and gave partial answers.
Moreover, I gave a mathematical formulation for the birth and spread model in the crystal growth, which is described by the forced mean curvature equations with source, and investigated asymptotic speed of solutions.
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| Free Research Field |
偏微分方程式論
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