Last modified on June/26/2016

Research



Meetings

* 界面運動,力学系に現れる漸近問題への粘性解的手法とその周辺」(日本語タイトル,本題) 英訳「Viscosity solution approach to asymptotic problems in front propagation, dynamical system and related topics」,2017 年 7 月 3 日 - 5 日,京都大学数理解析研究所. Program, Abstract,

Publications and Preprints

Book 1. Le Q. Nam, H. Mitake, H. V. Tran, Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampere Equations, Springer, Lecture Notes in Mathematics 2183, DOI 10.1007/978-3-319-54208-9. Link

26. (Joint work with K. Soga) Weak KAM theory for discount Hamilton-Jacobi equations and its application, submitted. PDF File

25. (Joint work with D. A. Gomes, and H. V. Tran) The Selection problem for discounted Hamilton-Jacobi equations: some non-convex cases, to appear in Journal of the Mathematical Society of Japan. PDF File

24. (Joint work with H. Ishii, and H. V. Tran) The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems, to appear in Journal de Mathematiques Pures et Appliquees. PDF File

23. (Joint work with H. Ishii, and H. V. Tran) The vanishing discount problem and viscosity Mather measures. Part 1: the problem on a torus, to appear in Journal de Mathematiques Pures et Appliquees. PDF File

22. (Joint work with Y. Giga, and 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. PDF File

21. (Joint work with A. Siconolfi, H. V. Tran, N. Yamada ) A Lagrangian approach to weakly coupled Hamilton-Jacobi systems, SIAM J. Math. Anal. 48 (2016), no. 2, 821--846. PDF File

20. (Joint work with H. V. Tran ) Selection problems for a discounted degenerate viscous Hamilton--Jacobi equation, Adv. Math. 306 (2017), 684--703. PDF File

19. (Joint work with D. A. Gomes) Existence for stationary mean field games with quadratic Hamiltonians with congestion, NoDEA Nonlinear Differential Equations Appl. 22 (2015), no. 6, 1897--1910. PDF File

18. (Joint work with H. V. Tran ) Weakly coupled systems of the infinity Laplace equations, Trans. Amer. Math. Soc. 369 (2017), 1773-1795. PDF File

17. (Joint work with H. V. Tran ) Large-time behavior for obstacle problems for degenerate viscous Hamilton-Jacobi equations, Calc. Var. Partial Differential Equations. 54, (2015), no. 2, 2039--2058. PDF File

16. (Joint work with F. Cagnetti, D. A. Gomes, and H. V. Tran ) A new method for large time behavior of degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians, Ann. Inst. H. Poincare Anal. Non Lineaire 32 (2015), no. 1, 183--200. PDF File

15. (Joint work with G. Barles and H. Ishii) A new PDE approach to the large time asymptotics of solutions of Hamilton--Jacobi equations, Bull. Math. Sci. 3 (2013), 363--388. PDF File

14. (Joint work with H. V. Tran ) A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton--Jacobi equations, J. Math. Pures Appl. 101 (2014) 76--93. PDF File

13. (Joint work with H. V. Tran ) Homogenization of weakly coupled systems of Hamilton-Jacobi equations with fast switching rates, Arch. Ration. Mech. Anal. 211 (2014), no. 3, 733--769. PDF File

12. (Joint work with G. Barles and H. Ishii) On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions, Arch. Ration. Mech. Anal. 204 (2012), 515--558. PDF File

11. (Joint work with H. V. Tran ) Remarks on the large time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton--Jacobi equations, Asymptot. Anal. 77 (2012), 43--70. PDF File

10. (Joint work with G. Barles ) A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi equations, Comm. Partial Differential Equations. 37 (2012), no. 1, 136–168. PDF File

9. (Joint work with Y. Giga and Q. Liu) Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton-Jacobi equations with non-coercive Hamiltonians, J. Differential Equations 252 (2012), no. 2, 1263-1282. PDF File

8. (Joint work with Y. Giga and Q. Liu) 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. PDF File

7. On convergence rates for solutions of approximate mean curvature equations, Proc. Amer. Math. Soc. 139 (2011), no. 10, 3691–3696. PDF File

6. (Joint work with G. Barles and O. Ley ) Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations, Math. Ann. 352 (2012), no. 2, 409--451. PDF File

5. Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data, Nonlinear Anal. 71 (2009), no. 11, 5392--5405. PDF File

4. (Joint work with H. Ishii) Two remarks on periodic solutions of Hamilton-Jacobi equations, World Scientific Publishing Co. Pte. Ltd., Toh Tuck Link, Singapore, pp. 97--119 (2009). PDF File

3. The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations. NoDEA Nonlinear Differential Equations App. 15 (2008), no. 3, 347--362. PDF File

2. Asymptotic solutions of Hamilton-Jacobi equations with state constraints, Appl. Math. Optim. 58 (2008), no. 3, 393--410. PDF File

1. (Joint work with H. Ishii), Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians, Indiana Univ. Math. J., 56 (2007), no. 5, 2159--2184. PDF File

Doctoral Dissertation.

Large Time Behavior of Solutions of Initial-Boundary Value Problems for Hamilton-Jacobi Equations, PhD thesis in Waseda University, March 2009. PDF File

Proceedings (no refereed)

6. H. Mitake, Large-time behavior of solutions to Hamilton-Jacobi equations with time-dependent boundary data, RIMS kokyuroku 1651, (2009), 48-57.

5. H. Mitake, Large time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations with periodic boundary data, Hokkaido University Technical Report Series in Mathematics 131 (2008), pp. 21--30.

4. H. Mitake, Asymptotic solutions of Hamilton-Jacobi equations with state constraints, Hokkaido University Technical Report Series in Mathematics 117 (2007) (JAPANESE).

3. H. Mitake, Asymptotic solutions of Hamilton-Jacobi equations with state constraints, RIMS kokyuroku, 1542 (2007), pp. 33--40.

2. H. Mitake, A representation formula for solutions of Hamilton-Jacobi equations, 27st Hatten-Houteisiki Wakate Seminar (2006), pp. 197--201 (JAPANESE).

1. H. Mitake, A representation formula for solutions of Hamilton-Jacobi equations, RIMS kokyuroku, 1481 (2006), pp. 32--42.

Visiting Career and Plan

3. Department of Mathematics, University of California, Berkeley (September 2010--August/2011). (Mentor: Lawrence Craig Evans)

2. Laboratoire de Mathematiques et Physique Theorique, Universite Francois Rabelais - Tours (May 2010--July 2010). (Mentor: Guy Barles)

1. Laboratoire de Mathematiques et Physique Theorique, Universite Francois Rabelais - Tours (April 2009--March 2010) (Mentor: Guy Barles).


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