Abstract
A singularly perturbed periodic problem for a parabolic reaction–diffusion–advection Burgers-type equation with modular advection and linear gain is considered. Conditions for the existence, uniqueness, and asymptotic Lyapunov stability of a periodic solution with an internal transition layer are obtained, and its asymptotic approximation is constructed. Asymptotic analysis is applied in solving the boundary control problem to achieve the required law of front’s motion. The concept of an asymptotic solution of this problem is formulated, sufficient conditions for the existence and uniqueness of the solution are obtained, and an asymptotic approximation of the solution is constructed.
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ACKNOWLEDGMENTS
We are grateful to the anonymous referee for a careful reading of the article and a number of valuable comments.
Funding
This work was supported by the Russian Science Foundation (project no. 18-11-00042).
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Translated by E. Chernokozhin
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Volkov, V.T., Nefedov, N.N. Asymptotic Solution of the Boundary Control Problem for a Burgers-Type Equation with Modular Advection and Linear Gain. Comput. Math. and Math. Phys. 62, 1849–1858 (2022). https://doi.org/10.1134/S0965542522110112
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DOI: https://doi.org/10.1134/S0965542522110112