研究業績

Navier-Stokes方程式関係

(査読有)

  1. H. Kikuchi, T. Kubo, R. Matsui, Existence of Weak Solution to the Navier-Stokes Equations Approximated by Pressure Stabilization Method,
    Journal of Mathematical Fluid Mechanics (2022), 24:80
  2. T. Kubo, Y. Shibata, On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface, Mathematics 9 (2021), no.6, 621: https://doi.org/10.3390/math9060621
  3. T. Kubo, R. Matsui, On pressure stabilization method for nonstationary Navier-Stokes equations, Communications on Pure and Applied Analysis, 17 (2018), no. 6, 2283–2307.
  4. T. Kobayashi, T. Kubo, K. Nakamura, On a Local Energy Decay Estimate of Solutions to the Hyperbolic type Stokes Equations, Journal of Differential Equations, 264 (2018), no. 10, 6061–6081.
  5. T. Kubo, Y. Shibata, K. Soga, On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface. Discrete and Continuous Dynamical Systems – Series A,(2016) 3741-3774
  6. T.Kobayashi, T.Kubo, Weighted Lp-Lq estimates of Stokes semigruoup in half-space and its application to the Navier-Stokes equations, Advances in Mathematical Fluid Mechanics, Recent Developments of Mathematical Fluid Mechanics,(2016). 337-350
  7. T. Hishida, T. Kubo, On the Asymtotic stability for small initial disturbance of Navier-Stokes flow in a two-dimensional aperture domain, Gakuto International Series, Mathematical Sciences and Application, Mathematical Fluid Dynamics and Nonlinear Wave, (2015) 183-192.
  8. T. Kubo, Y. Shibata, K. Soga, On the R-boundedness for the two phase problem: compressible-incompressible model problem, Boundary Value Problem, (2014):141, 33pp.
  9. T. Kobayashi, T. Kubo, Weighted Lp-Lq etimates of the Stokes semigroup in some unbounded domains, Tsukuba J. Math. Vol.37 No.2 (2013).179-205.
  10. T. Kobayashi, T. Kubo, Weighted estimates of Stokes semigroup in unbounded domains, Advanced studies in pure mathematics 64, Proceedings for the 4th MSJ-SI conference on Nonlinear Dynamics in Partial Differential Equations, (2015), 427-436
  11. T. Kubo, The Stokes and Navier-Stokes equations in an aperture domain, J. Math. Soc. Japan, Vol.59, No.3 (2007),837-859.
  12. T. Kubo, On the Stokes and Navier-Stokes equations in a perturbef half-space and an aperture domain, Asymptotic Analysis and Singularities, Hyperbolic and dispersive PDEs and uid mechanics, 47-1, Advanced Studies in Pure Mathematics, T. Kohno et al. ed. Tokyo Shoseki Printing Co. (2007), 169-187.
  13. T. Kubo and Y. Shibata, Lp – Lq estimate of the Stokes semigroup and its application to Navier-Stokes equation in a perturbed half-space, Hyperbolic Problems, Theory, Numerics and Applications, II, Asakura et al. ed. Yokohama Publishers (2006), 125-132.
  14. T. Kubo, Periodic solutions of the Navier-Stokes equations in a perturbed half-space and an aperture domain, Mathematical Methods in the Applied Sciences, 28, No.11 (2005), 1341-1357.
  15. T. Kubo and Y. Shibata, On some properties of solutions to the Stokes equation in the half-space and perturbed half-space. Equations in Math. Physics Quaderni in Mathematica, series edited by Dept. Math. II Univ. di Napoli 15 (2005), 151-220.
  16. T. Kubo and Y. Shibata, On the Stokes and Navier-Stokes ows in a perturbed half-space, Regularity and Other Aspects of the Navier-Stokes Equations, 　Vol. 70, Banach Center Publications (2005), 157-167.
  17. T. Kubo and Y. Shibata, On the Stokes and Navier-Stokes equations in a perturbed half-space, Advances in Differential Equations, Vol. 10, No.6 (2005), 695-720.

(査読無)

  1. T. Kubo, Analysis of non-stationary Navier-Stokes equations approximated by the pressure stabilization method, 研究集会”非圧縮性粘性流体の数理解析”,数理解析研究所講究録2107(2019),46-68.
  2. T. Kubo, On two phase problem: compressible -compressible model problem, 研究集会”非圧縮性粘性流体の数理解析”,数理解析研究所講究録1905(2014),61-72.
  3. T. Kubo, Weighted Lp -Lq estimate for the Stokes semigroup in half-space and perturbed half-space, 研究集会”流体と気体の数学解析”,数理解析研究所講究録1730 (2011), 1-17.
  4. T. Kubo, The Stokes and Navier-Stokes equations in an aperture domain, 研究集会”流体と気体の数学解析”, 数理解析研究所講究録1592 (2008), 53-68.
  5. T. Kubo and Y. Shibata, Lp – Lq estimate of the Stokes semigroup in a perturbed half-space, 研究集会”調和解析学と非線形偏微分方程式, 数理解析研究所講究録1389(2004),93-119.

時間遅れを含む微分方程式関係

    (査読有)

  1. T. Kubo, Y. Ueda, Existence theorem for global in time solutions to Burgers equation with a time delay, Journal of Differential Equations 333 (2022), 184-230

精度保証付き数値計算関係

(査読有)

  1. A.Takayasu, M. Mizuguchi, T. Kubo, and S. Oishi: “Accurate Method of Verified Computing for Solutions of Semilinear Heat Equatinos”, Reliable Computing, Vol.25, (2017), 74-99.
  2. M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi: “A method of verified computations for solutions to semilinear parabolic equations using semigroup theory”, SIAM J. Numer. Anal., Vol.55, No.2(2017)980-1001,
  3. M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi: “Numerical verification for existence of a global-in-time solution to semilinear parabolic equations”, Journal of Computational and Applied Mathematics, 315(2017)1-16.
  4. M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi: “On the embedding constant of the Sobolev type inequality for fractional derivatives”, NOLTA, IEICE, Vol.7, No.3(2016), 386-394.
  5. A. Takayasu, S. Oishi, T. Kubo,Numerical Existence Theorem for Solutions of Two-Point Boundary Value Problems of Nonlinear Differential Equations, NOLTA, IE-ICE, Vol.E93-N, No.10 (2010), 105-118.
  6. A. Takayasu, S. Oishi, T. Kubo,Computer assisted proofs of solutions to Nonlinear　elliptic partial differential equations, Proceedings of 2010 International Symposium　on Nonlinear Theory and its Applications (NOLTA 2010) (2010),135-138.
  7. A. Takayasu, S. Oishi, T. Kubo,A priori inverse operator estimation for guaranteed　error estimate, Proceedings of 4th Workshop on Reliable Engineering Computing　(REC2010) “Robust Design – Coping with Hazards, Risk and Uncertainty”,Singapore　(2010), 649-664.
  8. A. Takayasu, S. Oishi, T. Kubo,Guaranteed error estimate for solutions to two-point boundary value problem, Proceedings of 2009 International Symposium on　Nonlinear Theory and its Applications (NOLTA2009)(2009),214-217.
  9. A. Takayasu, S. Oishi, T. Kubo,Guaranteed error estimate for solutions to linear　two-point boundary value problems with FEM, Proceedings of ASIA SIMULATION　CONFERENCE 2009 (JSST 2009) (2009), Paper ID: 163.

(査読無)

  1. A. Takayasu, S. Oishi, T. Kubo, Numerical Existence Proofs and Guaranteed Error Bounds for Solutions to Two-Point Boundary Value Problems, 研究集会 数値解析と数値計算アルゴリズムの最近の展開,数理解析研究所講究録, 1719 (2010), 48-60.
  2. A. Takayasu, S. Oishi, T. Kubo,Numerical veri cation for solutions to nonlinear two-point boundary value problems with nite element method, Proceedings of the 24th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2009) (2009), 165-168.

その他

  1. N. Fukuda, T. Kinoshita and T. Kubo, “On the Galerkin-wavelet method for higher order differential equations, the Bulletin of the Korean Mathematical Society,Vol 50, No.3(2013),963-982.