MITAKE, Hiroyoshi

>personal home page
Associate Professor
Partial Differential Equation
Research interests
Viscosity solution approach to asymptotic problems in front propagation, dynamical system and related topics
Current research

The main subject of my research is nonlinear Partial Differential Equations (PDEs), and in particular I focus on the study of PDEs appearing in optimal control theory, differential game, mean field game, and geometric flow. More specifically, I have worked on Hamilon-Jacobi- Bellman equations, mean curvature equations, the system of HJB equations and Fokker-Planck equations, and related nonlinear PDEs, and got some of fundamental results in mathematical science. In particular, I am interested in several connections between PDEs and other fields. For instance, I have established a connection between stochastic optimal control and PDEs in terms of weak Kolmogorov-Arnold-Mose theory. Also, I am working on problems related to crystal growth and mean field games.

Selected publications
  1. H. Mitake, Asymptotic solutions of Hamilton-Jacobi equations with state constraints, Appl. Math. Optim. 58 (2008), no. 3, 393-410.
  2. G. Barles and H. Mitake, A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi equations, Comm. Partial Differential Equations 37 (2012), 136-168.
  3. Y. Giga, Q. Liu and H. Mitake, Singular Neumann problems and large- time behavior of solutions of non-coercive Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 366 (2014), no. 4, 1905-1941.
  4. F. Cagnetti, D. A. Gomes, H. Mitake, and H. V. Tran, A new method for large time behavior of degenerate viscous Hamilton-Jacobi quations with convex Hamiltonians, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 32 ( 2015), no. 1, 183-200.
  5. Y. Giga, H. Mitake, H. V. Tran, On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms, SIAM J. Math. Anal. 48 (2016), 3515-3546.
  6. H. Mitake, and H. V. Tran, Weakly coupled systems of the infinity Laplace equations, Trans. Amer. Math. Soc. 369 (2017), 1773-1795.
  7. H. Mitake, H. V. Tran, Selection problems for a discount degenerate viscous Hamilton-Jacobi equation, Adv. Math. 306 (2017), 684-703.
N. Q. Le, H. Mitake, H. V. Tran, Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge- Ampere Equations, Springer, Lecture Notes in Mathematics, 2183. Springer, Cham, 2017.

The Mathematical Society of Japan

MSJ Takebe Katahiro Prize for Encouragement of Young Researchers 2011