Kelvin-Voigt equations perturbed by anisotropic relaxation, diffusion and damping

摘要

The purpose of this work is the analysis of the existence and uniqueness of weak solutions to a Kelvin-Voigt problem wherein the viscous and relaxation parts of the stress tensor are given by distinct power-laws. We assume that the viscous and relaxation terms may be fully anisotropic and that the momentum equation is perturbed by a damping term which may also be fully anisotropic. In the particular case of considering this problem with a linear and isotropic relaxation term, we prove the existence of global and local weak solutions. The uniqueness of weak solutions is established in this case as well. For the full anisotropic problem, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients must interact in order to be established global and local in time a priori estimates. (C) 2019 Elsevier Inc. All rights reserved.