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Energy decay and propagation in a viscoelastic fluid with memory. (English) Zbl 1240.35402

Summary: A non-compressible viscoelastic fluid with memory is considered and the well posedness of the associated dynamical problem is studied. The exponential decay of the energy is obtained under suitable hypotheses on the memory kernel. Furthermore, a domain of dependence inequality is established, thereby showing the hyperbolic nature of the problem.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B40 Asymptotic behavior of solutions to PDEs
74A15 Thermodynamics in solid mechanics
74D05 Linear constitutive equations for materials with memory
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