Geodesic
On the global domain of influence of stable solutions with interior layers in the two-dimensional case
Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 1-40.

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We consider the initial-boundary problem for the singularly perturbed non-stationary reaction-diffusion equation with non-linearity of cubic type. We impose conditions sufficient for the existence of a stable stationary solution with an interior transition layer in the neighbourhood of a certain curve. We investigate the set of initial functions belonging to the domain of influence of this solution. 
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V. F. Butuzov; I. V. Nedelko. On the global domain of influence of stable solutions with interior layers in the two-dimensional case. Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 1-40. http://geodesic.mathdoc.fr/item/IM2_2002_66_1_a0/

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