带卷积和非线性条件的脉冲抛物整微分方程的混合问题

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s199508022460078x
A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev
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引用次数: 0

摘要

摘要 本文考虑了一个具有退化 kerneland 内卷的脉冲同调抛物型偏积分微分方程。关于空间变量 \(x\) 使用了 Dirichlet 边界值条件,并研究了谱问题。应用傅里叶变量分离法,得到了关于未知函数傅里叶系数的可数非线性函数方程组,证明了可数函数方程组唯一可解性定理。结合使用了连续逼近法和收缩映射法。以傅里叶级数形式得到了脉冲混合问题的唯一解。证明了傅里叶级数的绝对均匀收敛性。
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Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions

Abstract

In this paper, we consider an impulsive homogeneous parabolic type partial integro-differential equation with degenerate kernel and involution. With respect to spatial variable \(x\) is used Dirichlet boundary value conditions and spectral problem is studied. The Fourier method of separation of variables is applied. The countable system of nonlinear functional equations is obtained with respect to the Fourier coefficients of unknown function. Theorem on a unique solvability of countable system of functional equations is proved. The method of successive approximations is used in combination with the method of contraction mapping. The unique solution of the impulsive mixed problem is obtained in the form of Fourier series. Absolutely and uniformly convergence of Fourier series is proved.

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CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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