The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model

Shin-Ichiro Ei; Tohru Tsujikawa

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 625-633
  • ISSN: 0023-5954

Abstract

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Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in ℝ 2 and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates the shape of the solution in the neighborhood of the interface.

How to cite

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Ei, Shin-Ichiro, and Tsujikawa, Tohru. "The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model." Kybernetika 45.4 (2009): 625-633. <http://eudml.org/doc/37716>.

@article{Ei2009,
abstract = {Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in $\mathbb \{R\}^2$ and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates the shape of the solution in the neighborhood of the interface.},
author = {Ei, Shin-Ichiro, Tsujikawa, Tohru},
journal = {Kybernetika},
keywords = {reaction-diffusion system; interaction of fronts; phase transition model; bistability; motion of two interfaces},
language = {eng},
number = {4},
pages = {625-633},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model},
url = {http://eudml.org/doc/37716},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Ei, Shin-Ichiro
AU - Tsujikawa, Tohru
TI - The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 625
EP - 633
AB - Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in $\mathbb {R}^2$ and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates the shape of the solution in the neighborhood of the interface.
LA - eng
KW - reaction-diffusion system; interaction of fronts; phase transition model; bistability; motion of two interfaces
UR - http://eudml.org/doc/37716
ER -

References

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  8. Pattern formation for adsorbate-induced phase transition model, RIMS Kokyuroku Bessatsu B3 (2007), 43–58. MR2408125
  9. Standing wave patterns in the CO oxidation reaction on a Pt(110) surface: experiments and modeling, J. Phys. Chem. B 104 (2000), 3155–3178. 
  10. Numerical computations and pattern formation for adsorbate-induced phase transition model, Sci. Math. Japon. 61 (2005), 525–534. MR2140113
  11. Exponential attractor for an adsorbate-induced phase transition model in non smooth domains, Osaka J. Math. 43 (2006), 215–237. MR2222411
  12. Singular limit analysis of an adsorbate-induced phase transition model, Preprint. 
  13. Exponential attractor for an adsorbate-induced phase transition model, Kyushu J. Math. 56 (2002), 313–336. MR1934129

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