Bosello, Carlo Alberto; Lazzari, Barbara Energy decay and propagation in a viscoelastic fluid with memory. (English) Zbl 1240.35402 Differ. Integral Equ. 23, No. 3-4, 359-371 (2010). 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 Keywords:non-compressible viscoelastic fluid with memory; well posedness; exponential decay PDF BibTeX XML Cite \textit{C. A. Bosello} and \textit{B. Lazzari}, Differ. Integral Equ. 23, No. 3--4, 359--371 (2010; Zbl 1240.35402) OpenURL