具有卷积非线性的气体动力学Burgers方程

IF 0.2 Q4 MATHEMATICS
D. Serikbaev
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引用次数: 0

摘要

本文研究了一类具有Sturm-Liouville算子的弱非线性卷积型Burgers方程的初值问题。证明了该问题具有级数形式的显式解。为了实现我们的目标,我们使用了与数学各个领域相对应的方法,例如偏微分方程理论、数学物理和泛函分析。特别地,我们用傅里叶分析方法在Sobolev空间上证明了该问题解的存在性。据我们所知,这是卷积型Burgers方程得到的第一个结果。由于我们使用傅里叶分析方法,我们给出了傅里叶变换作用于卷积时的性质,同时也给出了Sturm-Liouville算子的分数阶性质。研究了具有初始柯西条件的卷积型弱非线性Burgers方程的广义解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Gas Dynamics type Burgers equation with convolutional nonlinearity
In this paper, we consider an initial value problem for the Burgers’ equation with convolution type weak nonlinearity for the Sturm–Liouville operator. We prove that this problem has an explicit solution in the form of series. To achieve our goals, we use methods that correspond to various fields of mathematics, such as the theory of partial differential equations, mathematical physics, and functional analysis. In particular, we use the Fourier analysis method to establish the existence of solutions to this problem on the Sobolev space. As far as we know, it is the first result obtained for the convolution type Burgers’ equation. Since, we use the Fourier analysis method we gave the properties of Fourier transform when acting on convolution, and also gave a property of fractional order of the Sturm–Liouville operator. The generalized solutions of the convolution type weak nonlinear Burgers’ equation with the initial Cauchy condition are studied.
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CiteScore
0.30
自引率
0.00%
发文量
11
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