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

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 o...

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Bibliographic Details
Published inDifferential equations Vol. 60; no. 2; pp. 180 - 203
Main Authors Turbin, M. V., Ustiuzhaninova, A. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2024
Springer Nature B.V
Subjects
Approximation
Boundary value problems
Difference and Functional Equations
Fixed points (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Schauder fixpoint theorem
weak solution
fluid with memory
modified Kelvin–Voigt model
initial–boundary value problem
trajectory
existence theorem
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Summary: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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266124020046