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.
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Original Russian Text © V.G. Zvyagin, V.P. Orlov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 2, pp. 215–220.
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Zvyagin, V.G., Orlov, V.P. On the weak solvability of the problem of viscoelasticity with memory. Diff Equat 53, 212–217 (2017). https://doi.org/10.1134/S0012266117020070
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DOI: https://doi.org/10.1134/S0012266117020070