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プロフィール

  • 氏名:柴田 将敬(Masataka SHIBATA)
  • 所属:東京工業大学 理学院
  • 担当:数学系・数学コース
  • 役職:助教
  • 研究分野:楕円型偏微分方程式、変分法、Mahler予想

担当の授業

2020年2Q

2020年1Q

過去の担当

http://www.math.titech.ac.jp/~shibata/lecture/を参照。

研究論文

  1. Kurata, Kazuhiro; Shibata, Masataka; "Least energy solutions to semi-linear elliptic problems on metric graphs". To appear in J. Math. Anal. Appl.

  2. Sato, Yohei; Shibata, Masataka; "Nonlinear scalar field equations with Berestycki-Lions' nonlinearity on large domains". To appear in Journal of Elliptic and Parabolic Equations.

  3. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "Uniqueness of asymptotic limit of ground states for a class of quasilinear Schrödinger equation with H^1-critical growth in R^3" To appear in Applicable Analysis.

  4. Naimen, Daisuke; Shibata, Masataka; "Existence and multiplicity of positive solutions of a critical Kirchhoff type elliptic problem in dimension four" Differential Integral Equations 33 (2020), no. 5-6, 223-246.

  5. Iriyeh, Hiroshi; Shibata, Masataka; "Symmetric Mahler's conjecture for the volume product in the 3-dimensional case". Duke Math. J. 169 (2020), no. 6, 1077-1134.

  6. Naimen, Daisuke; Shibata, Masataka; "Two positive solutions for the Kirchhoff type elliptic problem with critical nonlinearity in high dimension". Nonlinear Anal. 186 (2019), 187-208.

  7. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "Asymptotic property of ground states for a class of quasilinear Schrödinger equation with H^1-critical growth". Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 88, 29 pp.

  8. Sato, Yohei; Shibata, Masataka; "Infinitely many solutions for a nonlinear Schrödinger equation with general nonlinearity". Calc. Var. Partial Differential Equations 57 (2018), no. 5, Art. 137, 31 pp.

  9. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "A note on the uniqueness and the non-degeneracy of positive radial solutions for semilinear elliptic problems and its application". Acta Math. Sci. Ser. B (Engl. Ed.) 38 (2018), no. 4, 1121-1142.

  10. Shibata, Masataka; "A new rearrangement inequality and its application for L^2-constraint minimizing problems". Math. Z. 287 (2017), no. 1-2, 341–359.

  11. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "Global uniqueness results for ground states for a class of quasilinear elliptic equations". Kodai Math. J. 40 (2017), no. 1, 117–142.

  12. Sato, Yohei; Shibata, Masataka; "Existence of a positive solution for nonlinear Schrödinger equations with general nonlinearity". Adv. Nonlinear Anal. 3 (2014), suppl. 1, s55–s67.

  13. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations in R^2". Funkcial. Ekvac. 57 (2014), no. 2, 297–317.

  14. Shibata, Masataka; "Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term". Manuscripta Math. 143 (2014), no. 1-2, 221–237.

  15. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "Blow-up phenomena and asymptotic profiles of ground states of quasilinear elliptic equations with H^1-supercritical nonlinearities". J. Differential Equations 256 (2014), no. 4, 1492–1514.

  16. Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya; "Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations with general nonlinearities". Commun. Pure Appl. Anal. 13 (2014), no. 1, 97–118.

  17. Shibata, Masataka; "Asymptotic profile of a least-energy solution to a nonlinear elliptic equation in nonlinear optics". Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), no. 3, 619–646.

  18. Shibata, Masataka; "An existence result for some semi-linear elliptic equation in bent strip-like unbounded domains". Adv. Math. Sci. Appl. 15 (2005), no. 2, 587–601.

  19. Kurata, Kazuhiro; Watanabe, Tatsuya; Shibata, Masataka; "A symmetry-breaking phenomenon and asymptotic profiles of least-energy solutions to a nonlinear Schrödinger equation". Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), no. 2, 357–392.

  20. Kurata, Kazuhiro; Shibata, Masataka; Sakamoto, Shigeru; "Symmetry-breaking phenomena in an optimization problem for some nonlinear elliptic equation". Appl. Math. Optim. 50 (2004), no. 3, 259–278.

  21. Kurata, Kazuhiro; Shibata, Masataka; Tada, Kazuo; "Existence of positive solutions for some nonlinear elliptic equations on unbounded domains with cylindrical ends". Nonlinear Anal. 55 (2003), no. 1-2, 83–101.

  22. Shibata, Masataka; "Asymptotic shape of a solution for the plasma problem in higher dimensional spaces". Commun. Pure Appl. Anal. 2 (2003), no. 2, 259–275.

  23. Shibata, Masataka; "Asymptotic shape of a least energy solution to an elliptic free-boundary problem with non-autonomous nonlinearity". Asymptot. Anal. 31 (2002), no. 1, 1–42.

  24. Kurata, Kazuhiro; Shibata, Masataka; "On a one-dimensional variational problem related to the Cahn-Hilliard energy in a bent strip-like domain". Proceedings of the Third World Congress of Nonlinear Analysts, Part 2 (Catania, 2000). Nonlinear Anal. 47 (2001), no. 2, 1059–1068.

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