Abstract:
In this paper, we study a new class of time-periodic solutions with interior transition layer of reaction-advection-diffusion equations in the case of a fast reaction and a small diffusion. We consider the case of discontinuous sources (i.e., the nonlinearity describing the interaction and reaction) for a certain value of the unknown function that arise in a number of relevant applications. An existence theorem is proved, asymptotic approximations are constructed, and the asymptotic Lyapunov stability of such solutions as solutions of the corresponding initial-boundary-value problems is established.
Keywords:
reaction-advection-diffusion type equations, periodic parabolic boundary-value problems, singular perturbations, Burgers equations with modular advection, discontinuous sources, asymptotic method of differential inequalities, interior transition layer.
Citation:
N. N. Nefedov, “Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion”, Mat. Zametki, 112:4 (2022), 601–612; Math. Notes, 112:4 (2022), 588–597
\Bibitem{Nef22}
\by N.~N.~Nefedov
\paper Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 4
\pages 601--612
\mathnet{http://mi.mathnet.ru/mzm13732}
\crossref{https://doi.org/10.4213/mzm13732}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 4
\pages 588--597
\crossref{https://doi.org/10.1134/S0001434622090279}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140103674}
Linking options:
https://www.mathnet.ru/eng/mzm13732
https://doi.org/10.4213/mzm13732
https://www.mathnet.ru/eng/mzm/v112/i4/p601
This publication is cited in the following 7 articles:
V. S. Besov, V. I. Kachalov, “Holomorphic Regularization of Singularly Perturbed
Integro-Differential Equations”, Diff Equat, 60:1 (2024), 1
V. S Besov, V. I Kachalov, “GOLOMORFNAYa REGULYaRIZATsIYa SINGULYaRNO VOZMUShch¨ENNYKh INTEGRO-DIFFERENTsIAL'NYKh URAVNENIY”, Differencialʹnye uravneniâ, 60:1 (2024), 3
D. A. Maslov, “About One Method for Numerical Solution of the Cauchy Problem for Singularly Perturbed Differential Equations”, Comput. Math. and Math. Phys., 64:5 (2024), 1029
D. A Maslov, “ON A NUMERICAL METHOD FOR SOLVING THE CAUCHY PROBLEM FOR SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:5 (2024), 804
E. P. Kubyshkin, “Averaging Method in the Problem of Constructing Self-Oscillatory Solutions of Distributed Kinetic Systems”, Comput. Math. and Math. Phys., 64:12 (2024), 2868
V. I. Kachalov, D. A. Maslov, “Small Parameter Method in the Theory of Burgers-Type Equations”, Comput. Math. and Math. Phys., 64:12 (2024), 2886
V. I. Kachalov, D. A. Maslov, “Analyticity and pseudo-analyticity in the small parameter method”, Comput. Math. Math. Phys., 63:11 (2023), 1996–2004
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