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.
Classification : 35B25, 35B40, 35K40, 35K57, 74A50
Keywords: reaction-diffusion system; interaction of fronts; phase transition model 
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     author = {Ei, Shin-Ichiro and Tsujikawa, Tohru},
     title = {The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model},
     journal = {Kybernetika},
     pages = {625--633},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2009},
     mrnumber = {2588628},
     zbl = {1193.35006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a6/}
}
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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/