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Dive into the research topics where Takeshi Ohtsuka is active.

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Featured researches published by Takeshi Ohtsuka.


Journal of Scientific Computing | 2015

A Level Set Approach Reflecting Sheet Structure with Single Auxiliary Function for Evolving Spirals on Crystal Surfaces

Takeshi Ohtsuka; Yen-Hsi Richard Tsai; Yoshikazu Giga

We introduce a new level set method to simulate motion of spirals in a crystal surface governed by an eikonal–curvature flow equation. Our formulation allows collision of several spirals and different strength (different modulus of Burgers vectors) of screw dislocation centers. We represent a set of spirals by a level set of a single auxiliary function


Interfaces and Free Boundaries | 2006

On a uniform approximation of motion by anisotropic curvature by the Allen–Cahn equations

Yoshikazu Giga; Takeshi Ohtsuka; Reiner Schätzle


Mathematics for Nonlinear Phenomena: Analysis and Computation: International Conference in Honor of Professor Yoshikazu Giga on his 60th Birthday | 2015

Spatial Lipschitz Continuity of Viscosity Solution to Level Set Equation for Evolving Spirals by Eikonal-Curvature Flow

Takeshi Ohtsuka

u


Asymptotic Analysis | 2008

Motion of interfaces by an Allen-Cahn type equation with multiple-well potentials

Takeshi Ohtsuka


Preprint Series of Department of Mathematics, Hokkaido University | 2002

A level set method for spiral crystal growth

Takeshi Ohtsuka

u minus a pre-determined multi-valued sheet structure function


Discrete and Continuous Dynamical Systems - Series S | 2011

Optimal control problem for Allen-Cahn type equation associated with total variation energy

Takeshi Ohtsuka; Ken Shirakawa; Noriaki Yamazaki


Indiana University Mathematics Journal | 2008

Uniqueness and existence of generalized motion for spiral crystal growth

Shun'ichi Goto; Maki Nakagawa; Takeshi Ohtsuka

\theta


Crystal Growth & Design | 2018

Growth rate of crystal surfaces with several dislocation centers

Takeshi Ohtsuka; Yen-Hsi Richard Tsai; Yoshikazu Giga


Preprint Series of Department of Mathematics, Hokkaido University | 2012

A LEVEL SET APPROACH REFLECTING SHEET STRUCTURE WITH SINGLE AUXILIARY FUNCTION FOR EVOLVING SPIRALS ON CRYSTAL SURFACES

Takeshi Ohtsuka; Yen-Hsi Richard Tsai; Yoshikazu Giga

θ, which reflects the strength of spirals (screw dislocation centers). The level set equation used in our method for


arXiv: Analysis of PDEs | 2018

EXISTENCE OF ASYMPTOTIC SPEED OF SOLUTIONS TO BIRTH AND SPREAD TYPE NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Yoshikazu Giga; Hiroyoshi Mitake; Takeshi Ohtsuka; Tran Hung V.

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Yen-Hsi Richard Tsai

University of Texas at Austin

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