Polynomial decay rate for a new class of viscoelastic Kirchhoff equation related with Balakrishnan-Taylor dissipation and logarithmic source terms

In this paper, a polynomial decay rate of Kirchhoff s nonlinear viscoelastic viscoelastic equation solution related with Balakrishnan-Taylor dissipation solution and logarithmic source terms is obtained, where we obtain the result of energy decay of solutions without impose the usual relationship between certain relaxation functions and their derivatives. This result generalizes the previous results to an arbitrary decay rate, that is not necessarily of the polynomial or exponential decay. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.