On initial-boundary value problem for the Burgers equation in nonlinearly degenerating domain

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Applicable Analysis Pub Date : 2023-10-18 DOI:10.1080/00036811.2023.2271967

M. T. Jenaliyev, M. G. Yergaliyev

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Abstract

AbstractIn this paper, we study the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. In this paper, we found an orthonormal basis for domains with time-varying boundaries. On this basis, we use the Faedo–Galerkin method to prove theorems about the unique solvability of the problem under consideration. We also present some numerical results in the form of graphs of solutions to the problem under study for various initial data.Keywords: Burgers equationperiodic boundary conditionsdegenerating domainGalerkin methodMathematics Subject Classifications: 35K5535K1035R37 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research of the second author was supported by the grant of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Project AP13067805. The research of the first author was supported by the grant of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Project AP09258892.

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非线性退化域上Burgers方程的初边值问题

摘要本文研究了一类具有周期边界条件的Burgers方程初边值问题在非线性退化域上的可解性。本文给出了具有时变边界的域的一种标准正交基。在此基础上，我们利用Faedo-Galerkin方法证明了所考虑问题的唯一可解性定理。对于不同的初始数据，我们还以解法的形式给出了一些数值结果。关键词:Burgers方程周期边界条件退化域alerkin方法数学学科分类:35K5535K1035R37披露声明作者未报告潜在利益冲突。第二作者的研究得到了哈萨克斯坦共和国科学和高等教育部科学委员会项目AP13067805的资助。第一作者的研究得到了哈萨克斯坦共和国科学和高等教育部科学委员会项目AP09258892的资助。

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.