Abstract:
We study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a slow equation, which are usually called Tikhonov-type systems. A boundary layer asymptotics of solutions is constructed, the existence of solutions with this asymptotics is proved, and conditions for the Lyapunov asymptotic stability of these solutions treated as solutions of the corresponding initial–boudary value problems are obtained.
Citation:
N. N. Nefedov, “Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems”, Mat. Zametki, 115:2 (2024), 276–285; Math. Notes, 115:2 (2024), 232–239
\Bibitem{Nef24}
\by N.~N.~Nefedov
\paper Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction--Diffusion Systems
\jour Mat. Zametki
\yr 2024
\vol 115
\issue 2
\pages 276--285
\mathnet{http://mi.mathnet.ru/mzm14116}
\crossref{https://doi.org/10.4213/mzm14116}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4734359}
\transl
\jour Math. Notes
\yr 2024
\vol 115
\issue 2
\pages 232--239
\crossref{https://doi.org/10.1134/S000143462401022X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85190872378}
Linking options:
https://www.mathnet.ru/eng/mzm14116
https://doi.org/10.4213/mzm14116
https://www.mathnet.ru/eng/mzm/v115/i2/p276
This publication is cited in the following 2 articles:
E.I. Nikulin, N.N. Nefedov, A.O. Orlov, “Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities”, Russ. J. Math. Phys., 31:3 (2024), 504
N. N. Nefedov, “Existence and asymptotic behavior of solutions of boundary value problems for Tiknohov-type reaction–diffusion systems in the case of stability exchange”, Math. Notes, 116:6 (2024), 1332–1338
Citation in format AMSBIB
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