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Jenaliyev, M. T.; Yergaliyev, M. G.

On initial-boundary value problem for the Burgers equation in nonlinearly degenerating domain. (English) Zbl 07916269

Appl. Anal. 103, No. 11, 2003-2014 (2024).

MSC:

35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35R37 Moving boundary problems for PDEs

Keywords:

Burgers equation; periodic boundary conditions; degenerating domain; Galerkin method
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Full Text: DOI

References:

[1] Benia, Y, Sadallah, B-K.Existence of solutions to Burgers equations in a non-parabolic domain. Electron J Differ Equ. 2018;20:1-13. Available from: https://ejde.math.txstate.edu/Volumes/2018/20/benia.pdf · Zbl 1378.35261
[2] Benia, Y, Sadallah, B-K.A semilinear problem related to Burgers’ equation. Appl Anal. 2023;102(3):938-957. doi: · Zbl 1512.35385
[3] Jenaliyev, M, Ramazanov, M, Yergaliyev, M.On the coefficient inverse problem of heat conduction in a degenerating domain. Appl Anal. 2020;99(6):1026-1041. doi: · Zbl 1435.35192
[4] Jenaliyev, M, Ramazanov, M, Yergaliyev, M.On an inverse problem for a parabolic equation in a degenerate angular domain. Eurasian Math J. 2021;12:25-39. · Zbl 1488.65382
[5] Jenaliyev, M, Yergaliyev, M, Assetov, A.On one initial boundary value problem for the Burgers equation in a rectangular domain. Bull Karaganda Univ Math Ser. 2021;104(4):74-88. doi:
[6] Jenaliyev, MT, Assetov, AA, Yergaliyev, MG.On the solvability of the Burgers equation with dynamic boundary conditions in a degenerating domain. Lobachevskii J Math. 2021;42(15):3661-3674. doi: · Zbl 1486.35247
[7] Dkhil, F, Hamza, MA, Mannoubi, B.Asymptotic profiles for a class of perturbed Burgers equations in one space dimension. Opusc Math. 2018;38(1):41-80. doi: · Zbl 1402.35142
[8] Hasan, MT, Xu, C.The stability and convergence of time-stepping/spectral methods with asymptotic behaviour for the Rosenau-Burgers equation. Appl Anal. 2020;99(12):2013-2025. doi: · Zbl 1447.65023
[9] Chen, Y, Zhang, T.A weak Galerkin finite element method for Burgers’ equation. J Comput Appl Math. 2019;348:103-119. doi: · Zbl 1404.65164
[10] Lions, J-L, Magenes, E.Problemes aux limites non homohenes et apllications. Vol. 1. Paris: Dunod; 2003.
[11] Adams, RA, Fournier, JJF.Sobolev spaces. 2nd ed. Amsterdam: Elsevier; 2003. · Zbl 1098.46001
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