Asymptotics of solutions in the problem about small motions of a compressible Maxwell fluid. (English. Russian original) Zbl 1433.35310
Differ. Equ. 55, No. 9, 1150-1163 (2019); translation from Differ. Uravn. 55, No. 9, 1195-1208 (2019).
Summary: 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 \(C_0\)-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.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76A10 | Viscoelastic fluids |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35R09 | Integro-partial differential equations |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 74D05 | Linear constitutive equations for materials with memory |
| 74B05 | Classical linear elasticity |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 45R05 | Random integral equations |
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