List of Recent Publications

Papers

  • Computer assisted verification of the eigenvalue problem for one-dimensional Schrödinger operator, wit Ayuki Sekisaka, in Springer Proceeding in Mathematics. (Proceedings of Mathematical Challenge to a New Phase of Mater ials Science 2014)

  • Bifurcations of stationary solutions with triple junctions in phase separation problems --A new view of bifurcation analysis--, in Physica D 238 (2009), pp. 1050-1055.

  • An Infinite-dimensional Evans function theory for elliptic boundary value problems, with Jian Deng, in Jounal of Differential Equations 244 (2008), pp. 753-765.

  • Infinite dimensional Evans function theory for elliptic eigenvalue problems in a channel, with Jian Deng, in Jounal of Differential Equations 225 (2006), pp. 57-89.

  • Pitchfork and Hopf bifurcations of traveling pulses generated by coexisting front and back waves, in Methods and Applications of Analysis 7 (2000), pp. 615-640.

  • A topological approach to stability of pulses bifurcating from an inclination-flip homoclinic orbit, in Methods and Applications of Analysis 7 (2000), pp. 205-232.

  • Accumulation of eigenvalues in a stability problem, in Physica D 142 (2000), pp. 70-86.

  • A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations, in Jounal of Dynamics and Differential Equations 11 (1999), pp. 515-555.

  • Stability of travelling multiple-front (multiple-back) wave solutions of the FitzHugh-Nagumo equations, in SIAM Journal of Mathematical Analysis 28 (1997) pp.1094-1112.

  • An extension of the stability index for travelling wave solutions and its application to bifurcations in SIAM Journal of Mathematical Analysis 28 (1997) pp.402-433.

  • N-homoclinic bifurcations for homoclinic orbits changing their twisting, in Journal of Dynamics and Differential Equations 8 (1996) pp.549-572.

Proceedings

  • π1 and π2 theories of operators, in Problems in the Calculus of Variations and Related Topics (Kyoto, 2008). 数理解析研究所講究録(RIMS Kokyuroku) No. 1628 (2009), 58--62.

  • Travelling waves and linearised eigenvalue problem associated with them, in Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems (Sendai, 1997), 113--122, Tohoku Math. Publ., 8, Tohoku Univ., Sendai, 1998.

  • Stability and bifurcations of travelling waves of reaction diffusion equations, in Proceedings of the Korea-Japan Partial Differential Equations Conference (Taejon, 1996), 11 pp., Lecture Notes Ser., 39, Seoul Nat. Univ., Seoul, 1997.

  • An approach to eigenvalue problems associated with stability of travelling waves, in Differential equations and applications (Hangzhou, 1996), 249--257, Internat. Press, Cambridge, MA, 1997.

  • A topological approach to linear eigenvalue problems for travelling waves, in Study of partial differential equations by means of functional analysis (Kyoto, 1996). 数理解析研究所講究録(RIMS Kokyuroku) No. 969 (1996), 18--28.

  • N-homoclinic bifurcations for twisted homoclinic orbits, in Dynamical systems and chaos, Vol. 1 (Hachioji, 1994), 206--209, World Sci. Publishing, River Edge, NJ, 1995.

Surveys

  • 力学系におけるヘテロクリニック・ループの分岐と、反応拡散系等の方程式における進行波の分岐について, 日本数理生物学会ニュースレター No.56 (2008) pp.5-9

  • HomologyとConley Index 入門€, 物性研究 vol.78 (2002) pp.144-158

  • 進行波の線型安定性に対する位相的方法, 数学 51巻3号 (1999) pp.241-256 (English translation: Topological methods in stability analysis of travelling waves, in Amer. Math. Soc. Transl.(2), Vol. 204. (2001) pp. 45--62.)

Others

  • 数学と出会った頃--貴方は誰ですか？--, 数学セミナー2000年9月号 pp.73

Last updated: 21-Jun-2015