論文・著書

  学位論文

1. On the one-dimensional motion of the polytropic ideal gas with non-fixed boundary conditions,
   修士論文, 慶應義塾大学, 1985.
2. One-dimensional analysis for the motion of compressible viscous heat-conductive fluid,
   博士論文, 慶應義塾大学, 1988.
   

  論文 (レフェリー付きのもの)

1. On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary,
   J. Differential Equations 65 (1) (1986), 49-67.
2. On the outer pressure problem of the one-dimensional polytropic ideal gas,
   Japan J. Appl. Math. 5 (1) (1988), 53-85.
3. Global asymptotics of the outer pressure problem with free boundary,
   Japan J．Appl. Math. 5 (2) (1988), 205-224.
4. On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition,
   Quart. Appl. Math. 46 (4) (1988) 665-679.
5. Weak asymptotical stability of Yang-Mills' gradient flow (with K. Kono),
   Tokyo J. Math. 11 (2) (1988), 339-357.
6. On the one-dimensional free boundary problem for the heat-conductive compressible viscous gas,
   in "Recent Topics in Nonlinear PDE IV", Ed.: M. Mimura & T. Nishida, Lecture Notes in Num. Appl. Anal. 10, North-Holland/Kinokuniya, Tokyo, 1989, pp. 83-99.
7. Asymptotical stability of Yang-Mills' gradien flow,
   in "Geometry of Manifolds", Ed.:K. Shiohama, Perspect. Math. 8, Academic Press, Boston, 1989, pp. 499-517.
8. L_p,q-estimates for certain semi-linear parabolic equations,
   Tohoku Math. J. (2) 41 (4) (1989), 597-608.
9. Boundary value problems to a certain class of nonlinear diffusion equations,
   Math. Methods Appl. Sci. 14 (2) (1991), 79-92.
10. The rate of convergence for chemical interfacial reaction models,
    Funkcial. Ekvak. 35 (3) (1992), 515-531.
11. Discrete Morse semiflows of a functional with free boundary (with S. Omata),
    Adv. in Math. Sci. Appl. 2 (1) (1993), 147-187.
12. Uniqueness and Widder's theorems for the heat equation on Riemannian manifolds,
    in "Geometry and Its Applications", Ed.: T. Nagano, H. Omori, Y. Maeda & M. Kanai, World Scientific, Singapore, 1993, pp. 161-173.
13. An elementary proof of the blow-up phenomena for the heat equation with nonlinear boundary conditions,
    in "Nonlinear Partial Differential Equations", Ed.: G. Dong & F. Lin, International Academic Publisher, Beijing, 1993, pp. 197-204.
14. Discrete Morse semiflows and their convergence of a fuctional with free boundary (with S. Omata),
    in "Nonlinear Paftial Differential Equations", Ed.: G. Dong & F. Lin, International Academic Publisher, Beijing, 1993, pp. 205-213.
15. The set of solutions for certain semilinear heat equations,
    Tohoku Math. J. (2) 47 (1) (1995), 99-103.
16. Existence and asymptotic behavior of weak solutions to strongly damped semilinear hyperbolic system (with A. Tachikawa),
    Hokkaido Math. J. 24 (1) (1995), 387-405.
17. Existence and asymptotic behavior of weak solutions to semilinear hyperbolic systems with damped terms (with A. Tachikawa),
    Tsukuba J. Math. 20 (1) (1996), 51-64.
18. Weak solutions of a semilinear hyperbolic system on a nondecreasing domain (with A. Tachikawa),
    Math. Methods Appl. Sci. 19 (16) (1996), 1303-1316.
19. A variational method to construct weak solutions of nonlinear hyperbolic equations,
    in "Invited Lectures and Short Communications delivered at the Sixth International Colloquium on Differential Equations, Vol. I", Ed.: D. Bainov, Impulse-M, Plovdiv, 1996, pp. 279-287.
20. Navier-Stokes flow on Riemannian maniblds,
    Nonlinear Anal. 30 (2) (1997), 825-832.
21. Initial-final value problems for a ordinary differential equations and applications to equivariant harmonic maps (with K. Ueno),
    J. Math. Soc. Japan 50 (3) (1998), 545-555.
22. Numerical computations for a hyperbolic Ginzburg-Landau system (with K. Nakane & S.Omata),
    in "Invited Lectures delivered at the eighth International Colloquium on Differential Equations, Vol. II", Ed.: D. Kolev, Academic Publications, Plovdiv, 1998，pp. 89-97.
23. Construction of weak solutions of the Navier-Stokes equations on Riemannian manifold by minimizing variational functionals,
    Adv. in Math. Sci. Appl. 9 (1) (1999), 51-71.
24. Closed surfaces minimizing the bending energy under prescribed area and volume (with I. Takagi),
    in "International Conference on Differential Equations Berlin 1999, Vol. 1", Ed.: F. Fiedler, K. Groeger & J. Sprekels, World Scientic, Singapore, pp. 561-563, 2000.
25. Blow-up solutions for ordinary differential equations associated to harmonic maps and their applications (with A. Tachikawa),
    J. Math. Soc. Japan 53 (2) (2001), 485-500.
26. A new energy inequality and partial regularity for weak solutions of Navier-Stokes equations,
    J. Math. Fluid. Mech. 3 (1) (2001), 40-56.
27. A refinement of the energy inequality for the Navier-Stokes equations,
    Nonlinear Anal. 47 (6) (2001), 4245-4256.
28. Numerical computations for motion of vortices governed by a hyperbolic Ginzburg-Landau system (with K. Nakane & S. Omata),
    Nonlinear Anal. 51 (1) (2002), 67-77.
29. Bifurcating critical points of bending energy with constraints related to the shape of red blood cell (with I. Takagi),
    Calc. Var. Partial Differential Equations 16 (1) (2003), 63-111.
30. On the existence of solutions of the Helfrich flow and its center manifold near spheres (with Y. Kohsaka),
    Differential Integral Equations 19 (2), (2006), 121-142.
31. On the gradient flow for a shape optimization problem of plane curves as a singular limit (with T. Kurihara),
    Saitama Math. J. 24 (2006・2007), 43-75.

  著書

1. 基礎課程微分方程式 (吉野崇との共著), 培風館, 東京, 1996年.
2. 基礎微積分 (高橋豊文との共著), 学術図書, 東京, 2000年.
3. 基礎線形代数, 学術図書, 東京, 2003年.

  解説文

1. ICM98 偏微分方程式と応用数学関連の報告, 数学 51 (2) (1999), 205-207.
2. Equadiff 99 国際会議の報告 (坂元国望, 仙葉隆との共著), 応用数理 10 (1) (2000), 69-71.