The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions

Turbin, Mikhail Vyacheslavovich; Ustiuzhaninova, Anastasiya Sergeevna

doi:10.26907/0021-3446-2019-8-62-78

Iz. VUZ. Matematika

2019

DOI: 10.26907/0021-3446-2019-8-62-78

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The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions

Mikhail Vyacheslavovich Turbin¹,

Anastasiya Sergeevna Ustiuzhaninova²

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2024

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Solvability of initial-boundary value problem for the modified Kelvin–Voigt model with memory along trajectories of fluid motion

Turbin,

Ustiuzhaninova

2024

Differencialʹnye uravneniâ

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The work is devoted to proving the solvability in the weak sense of the initial-boundary value problem for the modified Kelvin–Voigt model taking into account memory along the trajectories of fluid particles motion. For this, an approximation problem is considered for which solvability is established based on the Leray–Schauder fixed point theorem. Then, based on a priori estimates, it is shown that from a sequence of solutions to the approximation problem, one can extract a subsequence that weakly converges to the solution of the original problem as the approximation parameter tends to zero.

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Solvability of initial-boundary value problem for the modified Kelvin–Voigt model with memory along trajectories of fluid motion

Turbin,

Ustiuzhaninova

2024

Differencialʹnye uravneniâ

View full text Add to dashboard Cite

show abstract

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The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions

Cited by 1 publication

References 2 publications

Solvability of initial-boundary value problem for the modified Kelvin–Voigt model with memory along trajectories of fluid motion

Solvability of initial-boundary value problem for the modified Kelvin–Voigt model with memory along trajectories of fluid motion

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