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Publishing Language: Chinese | Open Access

Periodic solutions to the steady viscous Burgers equation

Yuhan CAO1, Quansen JIU1( ), Luyao SHANG1, Yihong ZHANG2
School of Mathematical Sciences, Capital Normal University, Beijing 100048
Graduate School of Mathematics, Kyushu University, Fukuoka 819-0395
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Abstract

In this paper, the periodic solutions of the Burgers equation are expanded in a power series with respect to the viscosity coefficient ε which gives a recurrence relation among the approximate functions. Then, the general form of the Fourier expansions for the approximate functions are given by induction, and it is proved that the Fourier series of each approximate function is uniformly and absolutely convergent.

Keywords

Burgers equationperiodic solutionsFourier series

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Journal of Capital Normal University (Natural Science Edition)
Volume 45 Issue 1,
February 2024
Pages 60-67
DOI: 10.19789/j.1004-9398.2024.01.008

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CAO Y, JIU Q, SHANG L, et al. Periodic solutions to the steady viscous Burgers equation. Journal of Capital Normal University (Natural Science Edition), 2024, 45(1): 60-67. https://doi.org/10.19789/j.1004-9398.2024.01.008

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Received: 24 November 2023
Published: 01 February 2024
© The editorial department of Journal of Capital Normal University (Natural Science Edition) 2025.

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).