**学位論文**

- 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. - 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)**

- On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary,

J. Differential Equations 65 (1) (1986), 49-67. - On the outer pressure problem of the one-dimensional polytropic ideal gas,

Japan J. Appl. Math. 5 (1) (1988), 53-85. - Global asymptotics of the outer pressure problem with free boundary,

Japan J．Appl. Math. 5 (2) (1988), 205-224. - 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. - Weak asymptotical stability of Yang-Mills' gradient flow (with K. Kono),

Tokyo J. Math. 11 (2) (1988), 339-357. - 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. - Asymptotical stability of Yang-Mills' gradien flow,

in "Geometry of Manifolds", Ed.:K. Shiohama, Perspect. Math. 8, Academic Press, Boston, 1989, pp. 499-517. *L*-estimates for certain semi-linear parabolic equations,_{p,q}

Tohoku Math. J. (2) 41 (4) (1989), 597-608.- Boundary value problems to a certain class of nonlinear diffusion equations,

Math. Methods Appl. Sci. 14 (2) (1991), 79-92. - The rate of convergence for chemical interfacial reaction models,

Funkcial. Ekvak. 35 (3) (1992), 515-531. - Discrete Morse semiflows of a functional with free boundary (with S. Omata),

Adv. in Math. Sci. Appl. 2 (1) (1993), 147-187. - 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. - 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. - 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. - The set of solutions for certain semilinear heat equations,

Tohoku Math. J. (2) 47 (1) (1995), 99-103. - Existence and asymptotic behavior of weak solutions to strongly damped semilinear hyperbolic system (with A. Tachikawa),

Hokkaido Math. J. 24 (1) (1995), 387-405. - 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. - Weak solutions of a semilinear hyperbolic system on a nondecreasing domain (with A. Tachikawa),

Math. Methods Appl. Sci. 19 (16) (1996), 1303-1316. - 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. - Navier-Stokes flow on Riemannian maniblds,

Nonlinear Anal. 30 (2) (1997), 825-832. - 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. - 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. - 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. - 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. - 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. - A new energy inequality and partial regularity for weak solutions of Navier-Stokes equations,

J. Math. Fluid. Mech. 3 (1) (2001), 40-56. - A refinement of the energy inequality for the Navier-Stokes equations,

Nonlinear Anal. 47 (6) (2001), 4245-4256. - 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. - 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. - 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. - 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**

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

**解説文**

- ICM98 偏微分方程式と応用数学関連の報告, 数学 51 (2) (1999), 205-207.
- 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.

Last modified: Wed Jan 9 10:11:41 JST 2008