# Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system

Hiroshi Watanabe; Ken Shirakawa

Mathematica Bohemica (2014)

- Volume: 139, Issue: 2, page 381-389
- ISSN: 0862-7959

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topWatanabe, Hiroshi, and Shirakawa, Ken. "Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system." Mathematica Bohemica 139.2 (2014): 381-389. <http://eudml.org/doc/261891>.

@article{Watanabe2014,

abstract = {A one-dimensional version of a gradient system, known as “Kobayashi-Warren-Carter system”, is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a “stability” which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further, this is specified by using the notion of “energy-dissipative solution”, proposed in a relevant previous work.},

author = {Watanabe, Hiroshi, Shirakawa, Ken},

journal = {Mathematica Bohemica},

keywords = {approximation method; stability; energy-dissipative solution; approximation method; stability; energy-dissipative solution},

language = {eng},

number = {2},

pages = {381-389},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system},

url = {http://eudml.org/doc/261891},

volume = {139},

year = {2014},

}

TY - JOUR

AU - Watanabe, Hiroshi

AU - Shirakawa, Ken

TI - Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system

JO - Mathematica Bohemica

PY - 2014

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 139

IS - 2

SP - 381

EP - 389

AB - A one-dimensional version of a gradient system, known as “Kobayashi-Warren-Carter system”, is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a “stability” which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further, this is specified by using the notion of “energy-dissipative solution”, proposed in a relevant previous work.

LA - eng

KW - approximation method; stability; energy-dissipative solution; approximation method; stability; energy-dissipative solution

UR - http://eudml.org/doc/261891

ER -

## References

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