Japanese

T. Ohtsuka's web page

Division of Pure and Applied Sciences, Faculty of Science and Technology, Gunma University
4-2, Aramaki-machi, Maebashi, Gunma 371-8510, Japan

Publication list

Preprints

  1. WORK IN PROGRESS.
(old preprints)

Papers with review

  1. 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, to appear. (online first)
  2. 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, to appear.
  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.

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, RIMS Kôkyûroku No. 2121 Theoretical Developments to Phyenomenon Analysis based on Nonlinear Evolution Equations (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. (webpage on the report of "Emerging Developments in Interfaces and Free Boundaries")
  3. T. Ohtsuka, Evolution of crystal surface by a single screw dislocation with multiple spiral steps, RIMS Kôkyûroku No. 1924 Mathematical Analysis of Pattern Formation Arising in Nonlinear Phenomena (2014), 11-20. (pdf)
  4. 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)
  5. 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.
  6. T. Ohtsuka, Interface evolution by tristable Allen-Cahn equation with collision free condition, RIMS Kôkyûroku No. 1693 Nonlinear evolution equations and mathematical modeling (2010), 168-179. (pdf)
  7. T. Ohtsuka, Level set method for spiral crystal growth and surface evolution, Oberwolfach Reports 7(2010), 291-294.
  8. 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.
  9. T. Ohtsuka, Existence and uniqueness of level sets for spiral crystal growth, Proceedings in Applied Mathematics and Mechanics 7(2008), 1141503-1141504.
  10. T. Ohtsuka, The Allen-Cahn type equation with multiple-well potentials and mean curvature flow equation, RIMS Kôkyûroku No. 1545 Viscosity Solution Theory of Differential Equations and its Developments (2007), 38-46. (pdf)
  11. T. Ohtsuka, The uniqueness and existence of level sets for motion of spirals, RIMS Kôkyûroku No. 1542 Mathematical Models of Phenomena and Evolution Equation (2007), 123-135. (pdf)
  12. 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)
  13. 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.
  14. T. Ohtsuka, A level set method for a growth of a crystal by screw dislocation, RIMS Kôkyûroku No. 1287 Viscosity Solutions of Differential Equations and Related Topics (2002) 12-26.(pdf)