This article is cited in 2 scientific papers (total in 2 papers)
Existence and asymptotic behavior of solutions of boundary value problems for Tiknohov-type reaction–diffusion systems in the case of stability exchange
Abstract:
Singularly perturbed systems of reaction-diffusion equations in the case of
fast and slow equations,
known as Tikhonov-type systems, are studied.
The case where the roots of the
degenerate equation
intersect and hence are not isolated is considered.
Effective conditions for the existence of a solution whose approximation is the
so-called composite stable solution of the degenerate system are obtained.
The existence of a solution is proved and the accuracy of
the asymptotic approximation is estimated by using the
asymptotic method of differential inequalities extended to this class of problems.
Conditions for the Lyapunov stability of solutions such as
those of the corresponding initial boundary value problems are given.
Citation:
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”, Mat. Zametki, 116:6 (2024), 947–955; Math. Notes, 116:6 (2024), 1332–1338
\Bibitem{Nef24}
\by N.~N.~Nefedov
\paper Existence and asymptotic behavior of solutions of boundary value problems for Tiknohov-type reaction--diffusion systems in the case of stability exchange
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 6
\pages 947--955
\mathnet{http://mi.mathnet.ru/mzm14443}
\crossref{https://doi.org/10.4213/mzm14443}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 6
\pages 1332--1338
\crossref{https://doi.org/10.1134/S0001434624110397}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-86000447060}
Linking options:
https://www.mathnet.ru/eng/mzm14443
https://doi.org/10.4213/mzm14443
https://www.mathnet.ru/eng/mzm/v116/i6/p947
This publication is cited in the following 2 articles:
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