| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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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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