RESEARCH

PAPERS

1. H. Mitake, H. Watanabe, On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications, to appear in Proc. Amer. Math. Soc. Preprint is available from arXiv:2408.04960. 

2. H. Mitake, P. Ni, Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems, J. Differential Equations 440, Part 1, 25 (2025), 113442. https://doi.org/10.1016/j.jde.2025.113442. 

3. H. Mitake, H. V. Tran, Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals, Bull. Lond. Math. Soc. 57 (2025), no. 3, 748--770.  https://doi.org/10.1112/blms.13227

4. Y. Han, W. Jing, H. Mitake, H. V. Tran, Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications, Arch. Ration. Mech. Anal. 249 (2025), no. 2, Paper No. 18. https://doi.org/10.1007/s00205-025-02091-2

5. H. Mitake, Y. Oka, H. V. Tran, Quenching for axisymmetric hypersurfaces under forced mean curvature flows, Nonlinearity 38 (2025), no. 1, Paper No. 015010, 15 pp. https://doi.org/10.1088/1361-6544/ad9539

6. X. Bian, Y. Giga, H. Mitake, Distance comparison for curve shortening flow with a prescribed boundary, Advances in Mathematical Sciences and Applications, Vol. 34, No. 1 (2025), 101--113. 

7. H. Mitake, C. Mooney, H. V. Tran, J. Xin, Y. Yu, Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows, Math. Ann. 391 (2025), no. 2, 3077--3111. https://doi.org/10.1007/s00208-024-02983-w

8. X. Bian, Y. Giga, H. Mitake,   level-set method for a mean curvature flow with a prescribed boundary, Adv. Differential Equations 30 (2025), no. 1-2, 1--34. https://doi.org/10.57262/ade030-0102-1

9. T. Kagaya, Q. Liu, H. Mitake, A representation formula for viscosity solutions of nonlocal Hamilton-Jacobi equations and applications, SIAM J. Math. Anal. 56 (2024), no. 5, 5807--5839. https://doi.org/10.1137/23M1608136

10. H. Mitake, S. Sato, On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations, NoDEA Nonlinear Differential Equations Appl. 30 (2023) 30:68.  https://doi.org/10.1007/s00030-023-00880-w

11. T. Kagaya, Q. Liu, H. Mitake, Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations, NoDEA Nonlinear Differential Equations Appl. 30 (2023), no. 1, Paper No. 13, 28 pp. https://doi.org/10.1007/s00030-022-00818-8

12. H. Mitake, K. Terai, On weak solutions to first-order discount mean field games, Minimax Theory and its Applications 08 (2023), No. 1, 139--170. https://www.heldermann.de/MTA/MTA08/MTA081/mta08007.htm

13. J. Jang, D. Kwon, H. Mitake, H. V. Tran, Level-set forced mean curvature flow with the Neumann boundary condition,  J. Math. Pures Appl. (9) 168 (2022), 143--167. https://doi.org/10.1016/j.matpur.2022.11.002

14. D. A. Gomes, H. Mitake, H. V. Tran, The large time profile for Hamilton-Jacobi-Bellman equations,  Math. Ann. 384 (2022), no. 3-4, 1409--1459. https://doi.org/10.1007/s00208-021-02320-5

15. Y. Giga, H. Mitake, S. Sato, On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation,  J. Differential Equations 316 (2022), 364--386. https://doi.org/10.1016/j.jde.2022.01.057

16. H. Mitake, L. Zhang, Remarks on the generalized Cauchy-Dirichlet problem for graph mean curvature flow with driving force, Partial Differ. Equ. Appl. (2021) 2:40. https://doi.org/10.1007/s42985-020-00066-4

17. H. Mitake, H. V. Tran, T. S. Van, Large time behavior for a Hamilton-Jacobi equation in a critical Coagulation-Fragmentation model, Commun. Math. Sci. 19 (2021), no. 2, 495--512. https://dx.doi.org/10.4310/CMS.2021.v19.n2.a8

18. Y. Giga, H. Mitake, T. Ohtsuka, H. V. Tran,  Existence of asymptotic speed of solutions to birth and spread type nonlinear partial differential equations, Indiana Univ. Math. J. 70 (2021), no. 1, 121--156. https://doi.org/10.1512/iumj.2021.70.8305

19. H. Mitake, H. Ninomiya, K. Todoroki, A level set approach for multi-layered interface systems, Interfaces Free Bound. 22 (2020), no. 4, 383--400. https://doi.org/10.4171/IFB/444

20. D. A. Gomes, H. Mitake, K. Terai, The selection problem for some first-order stationary mean-field games,  Netw. Heterog. Media 15 (2020), no. 4, 681--710.  https://doi.org/10.3934/nhm.2020019

21. Y. Giga, Q. Liu, H. Mitake, Discrete schemes for time-fractional fully nonlinear evolution equations and their convergence,  Asymptot. Anal. 120 (2020), no. 1-2, 151--162. https://doi.org/10.3233/ASY-191583

22. W. Jing, H. Mitake, H. V. Tran, Generalized ergodic problems: existence and uniqueness structures of solutions,  J. Differential Equations 268 (2020), no. 6, 2886--2909. https://doi.org/10.1016/j.jde.2019.09.046

23. Y. Giga, H. Mitake, H. V. Tran,  Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 10, 3983--3999. https://doi.org/10.3934/dcdsb.2019228

24. H. Mitake, H. V. Tran, Y. Yu, Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting,  Arch. Ration. Mech. Anal. 233 (2019), no. 2, 901--934. https://doi.org/10.1007/s00205-019-01371-y

25. H. Mitake, K. Soga, Weak KAM theory for discount Hamilton-Jacobi equations and its application, Calc. Var. Partial Differential Equations 57 (2018), no. 3, Art. 78, 32 pp. https://doi.org/10.1007/s00526-018-1359-1

26. H. Mitake, H. V. Tran, On uniqueness sets of additive eigenvalue problems and applications, Proc. Amer. Math. Soc. 146 (2018), 4813--4822. https://doi.org/10.1090/proc/14152

27. D. A. Gomes, H. Mitake, H. V. Tran, The Selection problem for discounted Hamilton-Jacobi equations: some non-convex cases, J. Math. Soc. Japan 70 (2018), no. 1, 345--364.  DOI: 10.2969/jmsj/07017534

28. H. Ishii, H. Mitake, H. V. Tran, The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems, J. Math. Pures Appl. (9) 108 (2017), no. 3, 261--305. https://doi.org/10.1016/j.matpur.2016.11.002

29. H. Ishii, H. Mitake, H. V. Tran, The vanishing discount problem and viscosity Mather measures. Part 1: the problem on a torus,  J. Math. Pures Appl. (9) 108 (2017), no. 2, 125--149.  https://doi.org/10.1016/j.matpur.2016.10.013

30. H. Mitake, H. V. Tran, Selection problems for a discount degenerate viscous Hamilton--Jacobi equation, Adv. Math. 306 (2017), 684--703. https://doi.org/10.1016/j.aim.2016.10.032

31. H. Mitake, H. V. Tran, Weakly coupled systems of the infinity Laplace equations, Trans. Amer. Math. Soc. 369 (2017), 1773--1795. https://doi.org/10.1090/tran6694.

32. 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. https://doi.org/10.1137/15M1052755

33. H. Mitake, 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. https://doi.org/10.1137/15M1010841

34. D. A. Gomes, H. Mitake, Existence for stationary mean field games with quadratic Hamiltonians with congestion,   NoDEA Nonlinear Differential Equations Appl. 22 (2015), no. 6, 1897-1910. https://doi.org/10.1007/s00030-015-0349-7

35. H. Mitake, 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. https://doi.org/10.1007/s00526-015-0855-9

36. F. Cagnetti, D. A. Gomes, H. Mitake, H. V. Tran, A new method for large time behavior of degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians,  Ann. Inst. H. Poincar¥'e Anal. Non Lin¥'eaire 32 (2015), no. 1, 183--200. https://doi.org/10.1016/j.anihpc.2013.10.005. 

37. H. Mitake, 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. https://doi.org/10.1007/s00205-013-0685-x.

38. H. Mitake, 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. (9) 101 (2014), no. 1, 76--93. https://doi.org/10.1016/j.matpur.2013.05.004

39. Y. Giga, Q. Liu, 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. https://doi.org/10.1090/S0002-9947-2013-05905-3

40. G. Barles, H. Ishii, H. Mitake,  A new PDE approach to the large time asymptotics of solutions  of Hamilton--Jacobi equations, Bull. Math. Sci. 3 (2013), no. 3, 363--388. https://doi.org/10.1007/s13373-013-0036-0

41. H. Mitake, 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.  https://doi.org/10.3233/ASY-2011-1071

42. G. Barles, H. Ishii, H. Mitake, On the large time behavior of solutions of Hamilton--Jacobi equations associated with nonlinear boundary conditions, Arch. Ration. Mech. Anal.,  204 (2012), 515--558. https://doi.org/10.1007/s00205-011-0484-1

43. Y. Giga, Q. Liu, H. Mitake, Large-time asymptotics for one-dimensional Dirichlet problems for  Hamilton--Jacobi equations with non-coercive Hamiltonians, J. Differential Equations, 252, (2012), 1263--1282. https://doi.org/10.1016/j.jde.2011.10.010

44. G. Barles, 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. https://doi.org/10.1080/03605302.2011.553645

45. G. Barles, O. Ley, H. Mitake, Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations, Math. Ann. 352 (2012), 409--451. https://doi.org/10.1007/s00208-011-0648-1

46. H. Mitake, On convergence rates for solutions of approximate mean curvature equations, Proc. Amer. Math. Soc. 139 (2011), no. 10, 3691--3696. https://www.jstor.org/stable/41291932

47. H. Mitake, Large time behavior of solutions of Hamilton--Jacobi equations with periodic boundary data, Nonlinear Anal.  71  (2009),  no. 11, 5392--5405. https://doi.org/10.1016/j.na.2009.04.028

48. H. Mitake, 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. https://doi.org/10.1007/s00030-008-7043-y

49. H. Mitake, Asymptotic solutions of Hamilton--Jacobi equations with state constraints, Appl. Math. Optim. 58 (2008), no. 3, 393-410. https://doi.org/10.1007/s00245-008-9041-1

50. H. Ishii, H. Mitake, Representation formulas for solutions of Hamilton--Jacobi equations with convex Hamiltonians, Indiana Univ. Math. J., 56 (2007), no. 5, 2159--2184. https://doi.org/10.1512/iumj.2007.56.3048