On the weak solvability of the problem of viscoelasticity with memory


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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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