Uniqueness and existence of generalized motion for spiral crystal growth

Shun’ichi Goto, Maki Nakagawa, Takeshi Ohtsuka

Type: Article

Publication Date: 2008-01-01

Citations: 9

DOI: https://doi.org/10.1512/iumj.2008.57.3350

Abstract

We consider a level set equation of generalized mean curvature flow for spiral curves. It is shown that spiral curves described by the level set formulation are unique with respect to initial spiral curves. The method for constructing of an initial datum from the initial spiral curve is also proposed.

Locations

Indiana University Mathematics Journal - View
Hokkaido University Collection of Scholarly and Academic Papers (Hokkaido University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Uniqueness and existence of generalized motion for spiral crystal growth	2007	Shun’ichi Goto Maki Nakagawa Takeshi Ohtsuka
+ PDF Chat	Existence and uniqueness of level sets for spiral crystal growth	2007	Takeshi Ohtsuka
+	Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals	2023	Hiroyoshi Mitake Hung V. Tran
+	Asymptotic growth rate of solutions to level‐set forced mean curvature flows with evolving spirals	2024	Hiroyoshi Mitake Hung V. Tran
+ PDF Chat	Uniqueness and existence of spirals moving by forced mean curvature motion	2012	Nicolas Forcadel Cyril Imbert Régis Monneau
+	On spiral solutions to generalized crystalline motion with a rotating tip motion	2015	Tetsuya Ishiwata
+	The uniqueness and existence of level sets for motion of spirals(Mathematical Models of Phenomena and Evolution Equations)	2007	Takeshi Ohtsuka
+	The uniqueness and existence of level sets for motion of spirals(Mathematical Models of Phenomena and Evolution Equations)	2007	岳大塚
+ PDF Chat	Motion of spirals by crystalline curvature	1999	Hitoshi Imai Naoyuki Ishimura Takeo Ushijima
+	UNIQUENESS AND EXISTENCE FOR SPIRAL CRYSTAL GROWTH(Viscosity Solution Theory of Differential Equations and its Developments)	2007	Shun’ichi Goto
+	Spatial Lipschitz Continuity of Viscosity Solution to Level Set Equation for Evolving Spirals by Eikonal-Curvature Flow	2017	Takeshi Ohtsuka
+ PDF Chat	A minimizing movement approach for crystalline eikonal-curvature flows of spirals	2024	Takeshi Ohtsuka Yen‐Hsi Richard Tsai
+	Numerical analysis comparing ODE approach and level set method for evolving spirals by crystalline eikonal-curvature flow	2019	Tetsuya Ishiwata Takeshi Ohtsuka
+	NUMERICAL ANALYSIS COMPARING ODE APPROACH AND LEVEL SET METHOD FOR EVOLVING SPIRALS BY CRYSTALLINE EIKONAL-CURVATURE FLOW	2019	Tetsuya Ishiwata Takeshi Ohtsuka
+	Evolution of a spiral-shaped polygonal curve by the crystalline curvature flow with a pinned tip	2019	Tetsuya Ishiwata Takeshi Ohtsuka
+	On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms	2015	Yoshikazu Giga Hiroyoshi Mitake Hung V. Tran
+	On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms	2015	Yoshikazu Giga Hiroyoshi Mitake Hung V. Tran
+ PDF Chat	Towards modelling spiral motion of open plane curves	2015	Koichi Osaki Hirotoshi Satoh Shigetoshi Yazaki
+	Generalized motion by nonlocal curvature in the plane	2000	M.‐H Giga Yoshikazu Giga
+ PDF Chat	On Asymptotic Speed of Solutions to Level-Set Mean Curvature Flow Equations with Driving and Source Terms	2016	Yoshikazu Giga Hiroyoshi Mitake Hung V. Tran

Works That Cite This (7)

Action	Title	Year	Authors
+ PDF Chat	Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion	2015	Nicolas Forcadel Cyril Imbert Régis Monneau
+ PDF Chat	Uniqueness and existence of spirals moving by forced mean curvature motion	2012	Nicolas Forcadel Cyril Imbert Régis Monneau
+	Curvature flow with driving force on fixed boundary points	2017	Longjie Zhang
+	Spatial Lipschitz Continuity of Viscosity Solution to Level Set Equation for Evolving Spirals by Eikonal-Curvature Flow	2017	Takeshi Ohtsuka
+	Numerical analysis comparing ODE approach and level set method for evolving spirals by crystalline eikonal-curvature flow	2019	Tetsuya Ishiwata Takeshi Ohtsuka
+ PDF Chat	Growth Rate of Crystal Surfaces with Several Dislocation Centers	2018	Takeshi Ohtsuka Yen‐Hsi Richard Tsai Yoshikazu Giga
+	Asymptotic growth rate of solutions to level‐set forced mean curvature flows with evolving spirals	2024	Hiroyoshi Mitake Hung V. Tran

Works Cited by This (7)

Action	Title	Year	Authors
+	Spiral traveling wave solutions of some parabolic equations on annuli	2000	Toshiko Ogiwara Ken-Ichi Nakamura
+ PDF Chat	Spiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral crystal growth	2003	Toshiko Ogiwara Ken-Ichi Nakamura
+ PDF Chat	A LEVEL SET APPROACH TO SEMICONTINUOUS VISCOSITY SOLUTIONS FOR CAUCHY PROBLEMS	2001	Yoshikazu Giga Moto-Hiko Sato
+ PDF Chat	Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor	1995	Hitoshi Ishii Panagiotis E. Souganidis
+ PDF Chat	Motion of level sets by mean curvature. I	1991	L. C. Evans Joel Spruck
+ PDF Chat	Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations	1991	Yun Gang Chen Yoshikazu Giga Shun’ichi Goto
+ PDF Chat	Spiral Surface Growth without Desorption	1998	Alain Karma Mathis Plapp