Abstract
A model of a viscoelastic compressible Maxwell fluid is studied. This model is described by a system of partial integro-differential equations with appropriate boundary and initial conditions. An abstract analog of the problem under study is also considered. It is proved that a uniformly exponentially stable C0-semigroup emerges in this problem. Based on this fact, an estimate for the solution of the evolution problem is derived in the case where the external load is close to being almost periodic.
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Acknowledgments
The author is grateful to Prof. N.D. Kopachevskii for discussions of this work.
Funding
This work was supported by the Ministry of Education and Science of the Russian Federation, project no. 14.Z50.31.0037.
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Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 9, pp. 1195–1208.
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Zakora, D.A. Asymptotics of Solutions in the Problem about Small Motions of a Compressible Maxwell Fluid. Diff Equat 55, 1150–1163 (2019). https://doi.org/10.1134/S0012266119090040
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DOI: https://doi.org/10.1134/S0012266119090040