Geodesic
Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion
Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 601-612.

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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.
Mots-clés : reaction-advection-diffusion type equations, singular perturbations
Keywords: periodic parabolic boundary-value problems, Burgers equations with modular advection, discontinuous sources, asymptotic method of differential inequalities, interior transition layer. 
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N. N. Nefedov. Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion. Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 601-612. http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a8/

[1] N. N. Nefedov, “Razvitie metodov asimptoticheskogo analiza perekhodnykh sloev v uravneniyakh reaktsii-diffuzii-advektsii: teoriya i primenenie”, Zh. vychisl. matem. i matem. fiz., 61:12 (2021), 2074–2094 | DOI | Zbl

[2] O. V. Rudenko, “Neodnorodnoe uravnenie Byurgersa s modulnoi nelineinostyu: vozbuzhdenie i evolyutsiya intensivnykh voln”, Dokl. RAN, 474:6 (2017), 671–674 | MR | Zbl

[3] N. N. Nefedov, O. V. Rudenko, “O dvizhenii fronta v uravnenii tipa Byurgersa s kvadratichnoi i modulnoi nelineinostyu pri nelineinom usilenii”, Dokl. RAN, 478:3 (2018), 274–279 | MR | Zbl

[4] N. N. Nefedov, O. V. Rudenko, “O dvizhenii, usilenii i razrushenii frontov v uravneniyakh tipa Byurgersa s kvadratichnoi modulnoi nelineinostyu”, Dokl. AN, 493:1 (2020), 26–31 | Zbl

[5] A. Olchev, K. Radler, A. Sogachev, O. Panferov, G. Gravenhorst, “Application of a three-dimensional model for assessing effects of small clear-cuttings on radiation and soil temperature”, Ecological Model., 220:21 (2009), 3046–3056 | DOI

[6] N. Levashova, A. Sidorova, A. Semina, M. Ni, “A spatio-temporal autowave model of Shanghai territory development”, Sustainability, 11 (2019), 3658 | DOI

[7] A. Ya. Garaeva, A. E. Sidorova, V. A. Tverdislov, N. T. Levashova, “Model predposylok vidoobrazovaniya v predstavleniyakh teorii perkolyatsii i samoorganizovannoi kritichnosti”, Biofizika, 65:5 (2020), 932–948

[8] M. I. Budyko, “The effect of solar radiation variations on the climate of the Earth”, Tellus, 21:5 (1968), 611–619 | DOI

[9] J. I. Diaz, “Mathematical analysis of some diffusive energy balance models in climatology”, Mathematics, Climate and Environment, RMA Res. Notes Appl. Math., 27, Masson, Paris, 1993, 28–56 | MR | Zbl

[10] N. N. Nefedov, E. I. Nikulin, A. O. Orlov, “O periodicheskom vnutrennem sloe v zadache reaktsiya-diffuziya s istochnikom modulno-kubichnogo tipa”, Zh. vychisl. matem. i matem. fiz., 60:9 (2020), 1513–1532 | DOI | Zbl

[11] Yu. V. Bozhevolnov, N. N. Nefedov, “Dvizhenie fronta v parabolicheskoi zadache reaktsiya-diffuziya”, Zh. vychisl. matem. i matem. fiz., 50:2 (2010), 276–285 | MR

[12] P. C. Fife, L. Hsiao, “The generation and propogation of internal layers”, Nonlinear Anal., 12:1 (1998), 19–41 | DOI | MR

[13] A. I. Volpert, V. A. Volpert, “Traveling-wave solutions of parabolic systems with discontinuous nonlinear terms”, Nonlinear Anal., 49:1 (2002), 113–139 | DOI | MR | Zbl

[14] P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Res. Notes Math. Ser., 247, John Wiley and Sons, New York, 1991 | MR | Zbl

[15] A. B. Vasileva, V. F. Butuzov, Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Aktualnye voprosy prikladnoi i vychichslitelnoi matematiki, Vysshaya shkola, M., 1990 | MR | Zbl

[16] V. F. Butuzov, A. B. Vasileva, N. N. Nefedov, “Asimptoticheskaya teoriya kontrastnykh struktur (obzor)”, Avtomat. i telemekh., 1997, no. 7, 4–32 | MR | Zbl

[17] V. N. Pavlenko, “Silnye resheniya periodicheskikh parabolicheskikh zadach s razryvnymi nelineinostyami”, Differents. uravneniya, 52:4 (2016), 528–539 | MR

[18] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992 | MR | Zbl