On the weak solvability of the problem of viscoelasticity with memory
- Authors: Zvyagin V.G.1, Orlov V.P.1
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Affiliations:
- Voronezh State University
- Issue: Vol 53, No 2 (2017)
- Pages: 212-217
- Section: Partial Differential Equations
- URL: https://journals.rcsi.science/0012-2661/article/view/154279
- DOI: https://doi.org/10.1134/S0012266117020070
- ID: 154279
Cite item
Abstract
The existence of a weak solution is proved for a certain Oldroyd model of motion of a viscoelastic medium that allows for the memory of the system. The proof uses the theory of regular Lagrange flows and a topological approximation method that reduces the posed problem to an operator equation, its ε-regularization in smoother spaces, the use of a priori estimates and a topological degree for the proof of the solvability of the ε-regularized equations, and the passage to the limit as ε → 0.
About the authors
V. G. Zvyagin
Voronezh State University
Author for correspondence.
Email: zvg_vsu@mail.ru
Russian Federation, Voronezh, 394006
V. P. Orlov
Voronezh State University
Email: zvg_vsu@mail.ru
Russian Federation, Voronezh, 394006
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