Solvability of an Initial–Boundary Value Problem for the Modified Kelvin–Voigt Model with Memory along Fluid Motion Trajectories

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-06-05 DOI:10.1134/s0012266124020046

M. V. Turbin, A. S. Ustiuzhaninova

引用次数: 0

Abstract

The paper deals with proving the weak solvability of an initial–boundary value problem for the modified Kelvin–Voigt model taking into account memory along the trajectories of motion of fluid particles. To this end, we consider an approximation problem whose solvability is established with the use of the Leray–Schauder fixed point theorem. Then, based on a priori estimates, we show that the sequence of solutions of the approximation problem has a subsequence that weakly converges to the solution of the original problem as the approximation parameter tends to zero.

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具有流体运动轨迹记忆的修正开尔文-沃伊特模型初始边界值问题的可解性

摘要本文论证了修正的开尔文-沃伊特模型的初始边界值问题的弱可解性，并考虑了流体粒子运动轨迹的记忆。为此，我们考虑了一个近似问题，该问题的可解性是利用勒雷-肖德尔定点定理确定的。然后，基于先验估计，我们证明近似问题的解序列有一个子序列，当近似参数趋于零时，该子序列弱收敛于原始问题的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.