List of Publications

[Book]

  1. (with R.Gerard) Singular nonlinear partial differential equations, Aspects of Mathematics Vol. E 28, Vieweg-Verlag, Wiesbaden, Germany, 1996.

[List of articles]

  1. The Gevrey asymptotics in the initial value problem for singularly perturbed nonlinear differential equations, J. Differential Equations, 373 (2023), 283-326.
  2. Asymptotic existence theorem for formal solutions with singularities of nonlinear partial differential equations via multisummability, J. Math. Soc. Japan, Vol. 75, No. 3 (2023), 1055-1117.
  3. Uniqueness of the solution of some nonlinear singular partial differential equations of the second order, in Recent Trends in Formal and Analytic Solutions of Diff. Equations, Contemporary Mathematics, vol. 782, Amer. Math. Soc., Providence, RI, 2023, pp. 193-205.
  4. On a class of singular nonlinear first order partial differential equations, Tokyo J. Math., 45, No. 2 (2022), 333-359.
  5. Uniqueness of the solution of nonlinear singular first order partial differential equations, J. Math. Soc. Japan, 72, no. 4 (2020), 1259-1282.
  6. (with A. Lastra) Maillet type theorem for nonlinear totally characteristic partial differential equations, Mathematische Annalen, 377, issue 3-4 (2020), 1603-1641.
  7. On the summability of formal solutions of some linear $q$-difference-differential equations, Funkcialaj Ekvacioj, 63, no. 2 (2020), 259-291.
  8. (with H. Yamazawa) A note on $G_q$-summability of formal solutions of some linear $q$-difference-differential equations, RIMS Kokyuroku Bessatsu, B75 (2019), 113-121.
  9. (with Y. Okada and R. Shaefke) A formal solvability of a coupling equation for PDEs of Briot-Bouquet type, RIMS Kokyuroku, 2101 (2019), 91-97.
  10. (with D. B. Bacani and J. E. C. Lope) On the unique solvability of nonlinear Fuchsian partial differential equations, Tokyo J. Math., 41 (2018), 225-239.
  11. $q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials, Ann. Inst. Fourier, 67 (2017), no. 5, 1865-1903.
  12. Generalized Poincar\'e condition and convergence of formal solutions of some nonlinear totally characteristic equations, Tokyo J. Math., 39, no. 3 (2017), 863-883.
  13. (with Y. Okada and R. Sch\"{a}fke) Unique solvability of coupling equations in holomorphic functions, Several aspects of microlocal analysis, 69-78, RIMS Kokyuroku Bessatsu, B57 (2016)..
  14. (with M. A. C. Tolentino and D. B. Bacani) On the lifespan of solutions to nonlinear Cauchy problems with small analytic data, J. Differential Equations, 260 (2016), 897-922.
  15. Analytic continuation of solutions of some nonlinear convolution partial differential equations, Opuscula Math. 35, no. 5 (2015), 739-773.
    http://dx.doi.org/10.7494/OpMath.2015.35.5.739
  16. (with H. Yamazawa) q-Analogue of summability of formal solutions of some linear q-difference-differential equations, Opuscula Math. 35, no. 5 (2015), 713-738.
    http://dx.doi.org/10.7494/OpMath.2015.35.5.713
  17. (with D. B. Bacani) Unique solvability of some nonlinear partial differential equations with Fuchsian and irregular singularities, J. Math. Soc. Japan, 66 (2014), no. 3, 1017-1042.
  18. On a reduction of nonlinear partial differential dquations of Briot-Bouquet type, Tokyo J. Math., 36-2 (2013), 539-570.
  19. (with H. Yamazawa) Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations, J. Differential Equations, 255 (2013), 3592 - 3637.
  20. Time regularity in Gevrey classes of solutions to general nonlinear partial differential equations. Recent development of micro-local analysis for the theory of asymptotic analysis, 119-136, RIMS Kokyuroku Bessatsu, B40, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013.
  21. (with D. B. Bacani) On existence and uniqueness theorems for singular nonlinear partial differential equations. Recent development of micro-local analysis for the theory of asymptotic analysis, 69-79, RIMS Kokyuroku Bessatsu, B40, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013.
  22. (with H. Yamane) Nonlinear partial differential equations and logarithmic singularities. Exact WKB analysis and microlocal analysis, 203-209, RIMS Kokyuroku Bessatsu, B37, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013.
  23. Coupling of two singular partial differential equations and its application. Exact WKB analysis and microlocal analysis, 193-202, RIMS Kokyuroku Bessatsu, B37, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013.
  24. (with H. Yamazawa) Maillet type theorem, convolution equations and multisummability of formal solutions, RIMS Kokyuroku, 1861 (2013), 171-182.
  25. Maillet type theorem and Gevrey regularity in time of solutions to nonlinear partial differential equations, in: "Formal and analytic solutions of differential and difference equations", Banach center publications, 97 (2012), 125-140.
  26. (with D. B. Bacani) Existence and uniqueness theorem for a class of singular nonlinear partial differential equations, Publ. Res. Inst. Math. Sci., 48-4 (2012), 899-917.
  27. (with J. E. C. Lope, and M. Roque) On the unique solvability of certain nonlinear singular partial differential equations. Z. Anal. Anwend., 31 (2012), no. 3, 291-305.
  28. Gevrey regularity in time of solutions to nonlinear partial differential equations, J. Math. Sci. Univ. Tokyo, 18 (2011), 67-137.
  29. On the singularities of solutions of nonlinear partial differential equations in the complex domain, RIMS Kokyuroku, 1723 (2011), 101-109.
  30. Coupling of two partial differential equations and its application, II - the case of Briot-Bouquet type PDEs -, Publ. Res. Inst. Math. Sci., 45-2 (2009), 393-449.
  31. A sharp form of the uniqueness of the solution of nonlinear totally characteristic partial differential equations, Tokyo J. Math., 31-1 (2008), 195-202.
  32. (with H.Yamane) Logarithmic singularities of solutions to nonlinear partial differential equations, J. Math. Soc. Japan, 60-2 (2008), 603-630.
  33. Coupling of two partial differential equations and its application, Algebraic Analysis of Differential Equations (edited by T. Aoki, H. Majima, Y. Takei and N. Tose), 295-306, Springer, 2008.
  34. Coupling of two partial differential equations and its application, Publ. Res. Inst. Math. Sci., 43-3 (2007), 535-583.
  35. On the existence of holomorphic solutions of nonlinear partial differential equations in the complex domain (in Japanese), RIMS Kokyuroku, 1509 (2006), 51-61.
  36. Uniqueness of the solution of nonlinear totally characteristic partial differential equations, J. Math. Soc. Japan, 57 (2005), 1045-1065.
  37. Removable singularities of solutions of nonlinear totally characteristic type partial differential equations, RIMS Kokyuroku, 1431 (2005), 116-122.
  38. (with H.Yamazawa) Structure of solutions of nonlinear partial differential equations of Gerard-Tahara type, Publ. Res. Inst. Math. Sci., 41 (2005), 339-373.
  39. On the singularities of solutions of nonlinear partial differential equations in the complex domain, II. " Differential Equations and Asymptotic Theory in Mathematical Physics " (edited by H.Chen and R.Wong), 343-354, Series in Analysis Vol.2, World Sci., 2004.
  40. On the singularities of solutions of nonlinear partial differential equations in the complex domain, RIMS Kokyuroku, 1397 (2004), 102-111.
  41. Solvability of partial differential equations of nonlinear totally characteristic type with resonances, J. Math. Soc. Japan, 55 (2003), 1095-1113.
  42. (with T.Mandai) Structure of solutions to Fuchsian systems of partial differential equations, Nagoya Math. J., 169 (2003), 1-17.
  43. (with J.E.C.Lope) On the analytic continuation of solutions to nonlinear partial differential equations, J. Math. Pures Appl. 81 (2002), 811-826.
  44. On the singularities of solutions of nonlinear partial differential equations in the complex domain, "Microlocal Analysis and Complex Fourier Analysis" (edited by T.Kawai and K.Fujita), 273-283, World Sci., 2002.
  45. Solvability of non-linear totally characteristic partial differential equations in the complex domain - when resonances occur - RIMS Kokyuroku, 1261 (2002), 115-122.
  46. (with T.mandai) Structure of the solutions to Fuchsian systems, RIMS Kokyuroku, 1261 (2002), 68-77.
  47. (with J.E.C.Lope) A note on the analytic continuation of solutions to nonlinear partial differential equations, RIMS Kokyuroku, 1261 (2002), 56-67.
  48. (with H.Chen and Z.Luo) Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity, Ann. Inst. Fourier，Grenoble, 51 (2001), 1599-1620.
  49. On the singular solutions of nonlinear singular partial differential equations, RIMS Kokyuroku, 1211 (2001), 105-111.
  50. (with H.Chen and Z.Luo) Some new results on the nonlinear singular partial differential equations, "Partial differential equations and spectral theory : PDE2000 Conference in Clausthal, Germany" (edited by M.Demuth and B.-W.Schulze), 63-71, Birkhauser, Basel, 2001. Operator Theory: Advances and Applications, Vol. 126.
  51. On the singular solutions of nonlinear singular partial differential equations I, J. Math. Soc. Japan, 53 (2001), 711-729.
  52. (with H.Chen) On the holomorphic solution of non-linear totally characteristic equations, Math. Nachr., 219 (2000), 85-96.
  53. Uniqueness of the solution of nonlinear singular partial differential equations, "Partial differential equations and their applications" (edited by H.Chen and L.Rodino), 297-304, World Sci., 1999.
  54. (with H.Chen) On totally characteristic type non-linear partial differential equations in the complex domain, Publ. Res. Inst. Math. Sci., 35 (1999), 621-636.
  55. On the uniqueness theorem for nonlinear singular partial differential equations, 　RIMS Kokyuroku, 1090 (1999), 174-179.
  56. On the uniqueness theorem for nonlinear singular partial differential equations, J. Math. Sci. Univ. Tokyo, 5 (1998), 477-506.
  57. Nonlinear partial differential equations in the complex domain, 　RIMS Kokyuroku, 1028 (1998), 42-51.
  58. (with R.Gerard) Formal power series solutions of nonlinear first order partial differential equations, Funkcialaj Ekvacioj, 41 (1998), 133-166.
  59. Formal power series solutions of non-linear partial differential equations of the first order, RIMS Kokyuroku, 983 (1997), 133-141.
  60. (with R.Gerard) A new version of the factorization of a differential equation of the form F(x,y,Ty)=0, Proc. Japan Acad., 72 (1996), 218-220.
  61. On the uniqueness of the solution of singular nonlinear partial differential equations (in Japanese), RIMS Kokyuroku, 969 (1996), 12-17.
  62. Uniqueness of the solution of non-linear singular partial differential equations, J. Math. Soc.Japan, 48 (1996), 729-744.
  63. (with R.Gerard) On the factorization of an equation of the form F(x,y,Ty)=0 where T is a meromorphic vector field, "Structure of solutions of differential equations, Katata/Ktoto, 1995" (edited by Morimoto and Kawai), 151-167, World Sci., 1996.
  64. (with R.Gerard) Holomorphic and singular solutions of non-linear singular partial differential equations, II. "Structure of solutions of differential equations, Katata/Kyoto, 1995" (edited by Morimoto and Kawai), 135-150, World Sci., 1996.
  65. Removable singularities of solutions of nonlinear singular partial differential equations, "Singularities and differential equations", Banach Center Publications, 33 (1996), 395-399.
  66. (with R.Gerard) On the existence of holomorphic solutions of the Cauchy problem for nonlinear partial differential equations. Funkcialaj Ekvacioj, 37 (1994), 317-327.
  67. Holomorphic and singular solutions of nonlinear singular partial differential equations, RIMS Kokyuroku, 856 (1994), 136-141.
  68. (with R.Gerard) On the existence of holomorphic solutions of the Cauchy problem for nonlinear first order partial differential equations, J. Fac. Sci. Univ. Tokyo Sec. IA Math., 40 (1993), 549-560.
  69. (with R.Gerard) Solutions holomorphes et singulieres d'equations aux derivees partielles singulieres non lineaires. Publ. Res. Inst. Math. Sci., 29 (1993), 121-151.
  70. Singular hyperbolic systems, VIII. On the well-posedness in Gevrey classes for Fuchsian hyperbolic equations. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 39 (1992), 555-582.
  71. On singgular nonlinear first order partial differential equations of Briot-Bouquet type, RIMS Kokyuroku, 766 (1991), 55-58.
  72. (wirh R.Gerard) Theoreme du type Maillet pour une classe d'equations aux derivees partielles analytiques sigulieres, C. R. Acad. Sci. Paris, Serie I, 312 (1991), 499-502.
  73. (wirh R.Gerard) Holomorphic and singular solutions of nonlinear singular first order partial differential equations, Publ. Res. Inst. Math. Sci., 26 (1990), 979-1000.
  74. (wirh R.Gerard) Nonlinear singular first order partial differential equations of Briot-Bouquet type. Proc. Japan Acad., 66 (1990), 72-74.
  75. Solvability in distributions for a class of singular differential equations, III. Publ. Res. Inst. Math. Sci., 26 (1990), 185-196.
  76. Singular hyperbolic systems, VII. Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes (2) , Japan. J. Math., New Ser. 15 (1989), 275-307.
  77. Local solvability and boundary value problem for Fuchsian type partial differential equations (in Japanese), RIMS Kokyuroku, 675 (1988), 165-171.
  78. Solvability in distributions for a class of singular differential equations, II. Proc. Japan Acad., 64 (1988), 318-321.
  79. Solvability in distributions for a class of singular differential equations, I. Proc. Japan Acad., 64 (1988), 219-222.
  80. Fuchsian hyperbolic equations in Gevrey classes (2) (in Japanese), RIMS Kokyuroku, 660 (1988), 45-51.
  81. On the local solvability of Fuchsian type partial differential equations. Algebraic Analysis, Volume II (edited by M.Kashiwara and T.Kawai), 837-848, Academic Press, 1988.
  82. Local solvability of second order Fuchsian type equations, RIMS Kokyuroku, 638 (1988), 33-37.
  83. (with C.Parenti) Asymptotic expansions of distribution solutions of some Fuchsian hyperbolic equations. Publ. Res. Inst. Math. Sci., 23 (1987), 909-922.
  84. Singular hyperbolic systems, VI. Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes. J. Math. Soc. Japan, 39 (1987), 551-580.
  85. (with A.Bove, J.E.Lewis and C.Parenti) Cauchy problem for Fuchsian hyperbolic operators, II. J. Fac. Sci. Univ. Tokyo Sec. IA Math., 34 (1987), 127-157.
  86. Fuchsian hyperbolic equations in Gevrey classes, RIMS Kokyuroku, 591 (1986), 119-126.
  87. (with A.Bove, J.E.Lewis and C.Parenti) Singularities and Cauchy problem for Fuchsian hyperbolic equations. Proc. Japan Acad., 62 (1986), 80-82.
  88. On Fuchsian hyperbolic partial differential equations. Lecture Notes in Math. No. 1223, Springer, 1986, pp 243-253. (Proceedings of "Differential Equations in Banach Spaces" held in Bologna　(Italy), July 2-5, 1985.)
  89. Asymptotic expansions of solutions of Fuchsian hyperbolic equations in spaces of functions of Gevrey classes. Proc. Japan Acad., 61 (1985), 255-258.
  90. Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes. Proc. Japan Acad., 61 (1985), 63-65.
  91. Singular hyperbolic systems, V. Asymptotic expansions for Fuchsian hyperbolic partial differential equations. J. Math. Soc. Japan, 36 (1984), 449-473.
  92. Asymptotic expansions of solutions of Fuchsian hyperbolic partial differential equations. Proc. Japan Acad., 59 (1983), 120-121.
  93. Singular hyperbolic systems, IV. Remarks on the Cauchy problem for singular hyperbolic partial differential equations. Japan. J. Math., 8 (1982), 297-308.
  94. On a Volevic system of singular partial differential equations. J. Math. Soc. Japan, 34 (1982), 279-288.
  95. Fundamental systems of analytic solutions of Fuchsian type partial differential equations. Funkcialaj Ekvacioj, 24 (1981), 135-140.
  96. Singular hyperbolic systems, III. On the Cauchy problem for Fuchsian hyperbolic partial differential equations. J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 27 (1980), 465-507.
  97. On Fuchsian hyperbolic partial differential equations (in Japanese), RIMS Kokyuroku, 402 (1980), 126-154.
  98. Fuchsian hyperbolic equations and related topics (in Japanese), RIMS Kokyuroku, 376 (1980), 39-59.
  99. Singular hyperbolic systems, II. Pseudo-differential operators with a parameter and their applications to singular hyperbolic systems. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 391-412.
  100. Singular hyperbolic systems, I. Existence, uniqueness and differentiability. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 213-238.
  101. Fuchsian type equations and Fuchsian hyperbolic equations. Japan. J. Math., 5 (1979), 245-347.
  102. On the initial value problem for Fuchsian hyperbolic equations (in Japanese), RIMS Kokyuroku, 341 (1978), 164-172.
  103. Cauchy problems for Fuchsian hyperbolic partial differential equations. Proc. Japan Acad., 54 (1978), 92-96.
  104. The structure of local solutions of partial differential equations of the Fuchsian type, Publ. Res. Inst. Math. Sci., 12 Suppl. (1977), 465-468.
  105. Frobenius method in Fuchsian type partial differential equations (in Japanese), RIMS Kokyuroku, 281 (1976), 176-191.
  106. Structure of hyperfunction solutions of Fuchsian hyperbolic equations (in Japanese), RIMS Kokyuroku, 266 (1976), 142-175.
  107. Fuchsian hyperbolic equations (in Japanese), RIMS Kokyuroku, 248 (1975), 16-59.
    108.
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