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The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model. (English) Zbl 1193.35006
Summary: M. Hildebrand et al. [Phys. Rev. Lett. 83, 1475–1478 (1999)] proposed an adsorbate-induced phase transition model. For this model, Y. Takei et al. [Sci. Math. Jpn. 61, No. 3, 525–534 (2005; Zbl 1081.37541)] 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.
##### MSC:
 35B25 Singular perturbations in context of PDEs 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs 35K45 Initial value problems for second-order parabolic systems 35K58 Semilinear parabolic equations
##### Keywords:
bistability; motion of two interfaces
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##### References:
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