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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.
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
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