# On Asymptotics for the Solution of a Singularly Perturbed Parabolic Problem with a Multizone Internal Transition Layer

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### Abstract

For a singularly perturbed parabolic equation with Neumann boundary conditions, we construct and substantiate asymptotics of a time-periodic solution possessing a multizone internal transition layer. Multizonality of the transition layer is caused by the fact that the degenerate equation has three nonintersecting roots, two of which are simple and the third one has multiplicity two. The asymptotic decomposition of the solution is qualitatively different from the well-known decomposition in the case when all the three roots of the degenerate equation are simple.

## Keywords:

parabolic problem internal transition layer asymptotic solution steplike contrast structure.## Notes

### ACKNOWLEDGMENTS

This work was partially supported by the Russian Foundation for Basic Research, project no. 15-01-04619.

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