Antontsev, S Nde Oliveira, H. B.Khompysh, Kh2020-09-232020-09-2320191742-6596http://hdl.handle.net/10400.1/14738Generalized Kelvin-Voigt equations governing nonhomogeneous and incompressible fluids are considered in this work. We assume that, in the momentum equation, the diffusion and relaxation terms are described by two distinct power-laws. Moreover, we assume that the momentum equation is perturbed by an extra term, which, depending on whether its signal is positive or negative, may account for the presence of a source or a sink within the system. For the associated initial-boundary value problem, we study the existence of weak solutions as well as the large time behavior of the solutions.engKelvin-Voigtjournal article10.1088/1742-6596/1268/1/012008