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大塚岳のwebページ

群馬大学 情報学部 准教授(所属が変わりました)
〒371-8510 群馬県前橋市荒牧町4-2
メールアドレス: 論文中のメールアドレスをご覧下さい.
いろいろテスト運用中。Ver. 2
試験的にGoogle Scholarへのリンクを載せてみるなど。
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研究内容

非線形偏微分方程式論, 応用数学, 数値解析
界面の発展現象の解析, 等高面法, 反応拡散方程式, 粘性解理論, 最適制御問題など

Publication list

Google Scholar

Preprints

  1. T. Ohtsuka, Y.-H. R. Tsai, A minimizing movement approach for crystalline eikonal-curvature flows of spirals, arXiv:2409.16421(2024).
(old preprints)

Papers with review

  1. Y. Giga, H. Mitake, T. Ohtsuka, and H. V. Tran, Existence of asymptotic speed of solutions to birth and spread type nonlinear partial differential equations, Indiana University Mathematics Journal, 70(2021), no. 1, 121-156. (web page)
  2. T. Ishiwata and T. Ohtsuka, Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow, Discrete and Continuous Dynamical Systems Series S, 14(2021), no. 3, 893-907. (web page)
  3. T. Ishiwata and T. Ohtsuka, Evolution of spiral-shaped polygonal curve by crystalline curvature flow with a pinned tip, Discrete and Continuous Dynamical Systems Series B 24(2019), no. 10, 5261-5295. (web page)
  4. T. Ohtsuka, Y.-H. R. Tsai, and Y. Giga, Growth rate of crystal surfaces with several dislocation centers, Crystal Growth & Design 18(2018), no. 3, 1917-1929. (web page)
  5. T. Ohtsuka, Spatial Lipschitz continuity of viscosity solution to level set equation for evolving spirals by eikonal-curvature flow, Mathematics for Nonlinear Phenomena: Analysis and Computation. Springer Proceedings in Mathematics & Statistics 215(2017), 241-260. (web page)
  6. T. Ohtsuka, Y.-H. R. Tsai and Y. Giga, A level set approac reflecting sheet structure with single auxiliary function for evolving spirals on crystal surface, Journal of Scientific Computing 62(2015), no. 3, 831-874. (web page)
  7. T. Ohtsuka, Discontinuous stationary solution to generalized eikonal-curvature equation and its stability, Commentarii Mathematici Universitas Sancti Pauli 63(2014), no. 1-2, 233-260.
  8. M.-H. Giga, Y. Giga, T. Ohtsuka and N. Umeda, On behavior of signs for the heat equation and a diffusion method for data separation, Communications on Pure and Applied Analysis 12(5) (2013), no. 5, 2277-2296. (web page)
  9. T. Ohtsuka, K. Shirakawa and N. Yamazaki, Optimal control problem for Allen-Cahn type equation associated with total variation energy, A special volume of Discrete and Continuous Dynamical Systems - Series S "PDE approximations in Fast reaction - Slow diffusion scenarios" 5(2012), no. 1, 159-181. (web page)
  10. S. Goto, M. Nakagawa and T. Ohtsuka, Uniqueness and existence of generalized motion for spiral crystal growth, Indiana University Mathematics Journal 57(2008), no. 5, 2571-2599. (web page)
  11. T. Ohtsuka, The singular limit of an Allen-Cahn type equation with unbalanced multiple-well potential, International Conference for the 25th Anniversary of Viscosity solutions, Gakuto International Series Mathematical Sciences and Applications 30(2008), 165-174.
  12. T. Ohtsuka, K. Shirakawa and N. Yamazaki, Convergence of numerical algorithm for optimal control problem of Allen-Cahn type equation with constraint, Proceedings of International Coference on: Nonlinear Phenomena with Energy Dissipation, Mathematical Analysis, Modeling and Simulation, Gakuto International Series Mathematical Sciences and Applications 29(2008), 441-462.
  13. T. Ohtsuka, Numerical simulations for optimal controls of an Allen-Cahn type equation with constraint, Proceedings of International Coference on: Nonlinear Phenomena with Energy Dissipation, Mathematical Analysis, Modeling and Simulation, Gakuto International Series Mathematical Sciences and Applications 29(2008), 329-339.
  14. T. Ohtsuka, K. Shirakawa and N. Yamazaki, Optimal control of a singular diffusion equation with constraint, Advances in Mathematical Sciences and Applications 18(2008), no. 1, 1-28.
  15. T. Ohtsuka, Motion of interfaces by an Allen-Cahn type equation with multiple-well potentials, Asymptotic Analysis 56(2008), no. 2, 87-123.
  16. Y. Giga, T. Ohtsuka and R. Schätzle, On a uniform approximation of motion by anisotropic curvature by Allen-Cahn equation, Interfaces and Free boundaries 8(2006), no. 3, 317-348. (web page)
  17. T. Ohtsuka, A level set method for spiral crystal growth, Advances in Mathematical Sciences and Applications 13(2003), no. 1, 225-248.

論文(和文)

  1. 大塚岳, スパイラル成長の等高線法とその応用, 応用数理, 33(2023), no.3, 121-132.

Proceedings or abstracts (without review)

  1. T. Ohtsuka, Minimizing movement approach without using distance function for evolving spirals by the crystalline curvature with driving force, 数理解析研究所講究録 No. 2121 非線形発展方程式を基盤とする現象解析に向けた数学理論の展開 (2019), 74-87. (pdf)
  2. T. Ohtsuka, Minimizing movement approach for spirals evolving by crystalline curvature using level set functions, Oberwolfach Reports 14(2017), 314-317. (報告集へのリンク)
  3. 大塚岳, 渦巻成長のインアクティブペアにおける成長上限と定常解の構成について, 第36回発展方程式若手セミナー報告集 (2014), 35-43.
  4. T. Ohtsuka, Evolution of crystal surface by a single screw dislocation with multiple spiral steps, 数理解析研究所講究録 No. 1924 非線形現象に現れるパターン形成の数理解析 (2014), 11-20. (pdf)
  5. 大塚岳, 幾何学的発展方程式に対する等高面の方法, 応用数学勉強会2013 @芝浦工大 レクチャーノート(web page), 2014. 近いうちに改訂版出します! と言い続けてはや何年。
  6. T. Ohtsuka, Stability of bunched spirals and inactive pair in evolution of spirals with an eikonal-curvature flow, Oberwolfach Reports 10(2013), 915-918. (web page)
  7. T. Ohtsuka, Evolution of spirals by an eikonal-curvature flow equation with a single level set formulation, Proceedings of the 37th Sapporo Symposium on Partial Differential Equations -In memory of Professor Rentaro Agemi-, Hokkaido University Technical Report Series in Mathematics #153 (2012), 62-71.
  8. T. Ohtsuka, Interface evolution by tristable Allen-Cahn equation with collision free condition, 数理解析研究所講究録1693 非線形発展方程式と現象の数理 (2010), 168-179. (pdf)
  9. T. Ohtsuka, Level set method for spiral crystal growth and surface evolution, Oberwolfach Reports 7(2010), 291-294.
  10. T. Ohtsuka, A level set method for spiral crystal growth and growth rate of crystal surface, Proceedings of minisemester on evolution of interfaces Sapporo 2010, Hokkaido University Technical Report Series in Mathematics #145 (2010), 57-61.
  11. T. Ohtsuka, Existence and uniqueness of level sets for spiral crystal growth, Proceedings in Applied Mathematics and Mechanics 7(2008), 1141503-1141504. (web page)
  12. T. Ohtsuka, The Allen-Cahn type equation with multiple-well potentials and mean curvature flow equation, 数理解析研究所講究録1545 微分方程式の粘性解理論とその発展 (2007), 38-46. (pdf)
  13. T. Ohtsuka, The uniqueness and existence of level sets for motion of spirals, 数理解析研究所講究録1542 現象の数理モデルと発展方程式, (2007), 123-135. (pdf)
  14. T. Ohtsuka, On the singular limit of anisotropic Allen-Cahn equation approximating anisotropic mean curvature flow with driving force term, Proceedings of the 29th Sapporo Symposium on Partial Differential Equations, Hokkaido University Technical Report Series in Mathematics #84 (2004), 59-68. (web page)
  15. T. Ohtsuka, Uniform estimate for a solution of anisotropic Allen-Cahn equation, Proceedings of the Twelfth Tokyo Conference on Nonlinear PDE 2003 (2004), 1-12.
  16. T. Ohtsuka, A level set method for a growth of a crystal by screw dislocation, 数理解析研究所講究録1287 微分方程式の粘性解とその周辺, (2002) 12-26.(pdf)

Movies

  1. Talk on "Minimizing movement approach using general level set functions for evolving spirals by crystalline curvature flow"
    2018年6月 Banff International Research Stationにて新たな黒歴史がまた1ページ.
  2. Presentations in SIAM Conference on Mathematical Aspects of Materials Science
    2013年6月、フィラデルフィアにて開催されたSIAM研究集会
    "SIAM Conference on Mathematical Aspects of Materials Science"
    の講演動画集。
    この中に大変拙い私の講演がありますが、本人は1分も聞いていられなかったと述べておきます。

雑記

研究含む数学や自分の趣味を含む, ちょっとした話. 基本的に茶呑み話なので, 正確性だとか学術性だとか 高尚なものは余り期待しないで下さい.
(別ページに飛びます.)

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