Geodesic
The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model
Kybernetika, Tome 45 (2009) no. 4, pp. 625-633
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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 $\mathbb{R}^2$ 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.
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.
Classification : 35B25, 35B40, 35K40, 35K57, 74A50
Keywords: reaction-diffusion system; interaction of fronts; phase transition model 
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Ei, Shin-Ichiro; Tsujikawa, Tohru. The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model. Kybernetika, Tome 45 (2009) no. 4, pp. 625-633. http://geodesic.mathdoc.fr/item/KYB_2009_45_4_a6/

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