Abstract
A singularly perturbed periodic problem for a parabolic reaction-advection-diffusion equation at low advection is studied. The case when there is an internal transition layer under unbalanced nonlinearity is considered. An asymptotic expansion of a solution is constructed. To substantiate the asymptotics thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is studied; the proof uses the Krein-Rutman theorem.
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The work was supported by Russian Foundation for Basic Research under grants nos. 13-01-00200 and 14-01-91333.
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Nefedov, N.N., Nikulin, E.I. Existence and stability of periodic contrast structures in the reaction-advection-diffusion problem. Russ. J. Math. Phys. 22, 215–226 (2015). https://doi.org/10.1134/S1061920815020089
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DOI: https://doi.org/10.1134/S1061920815020089