On the Neumann-Dirichlet problem for a system of nonlinear viscoelastic equations of Kirchhoff type with Balakrishnan- Taylor term

By Bui Duc Nam, Huynh Van Dung, Le Tuan Khai
DOI: 10.37550/tdmu.EJS/2023.05.416

In this paper, the Neumann-Dirichlet boundary problem for a system of nonlinear viscoelastic
equations of Kirchhoff type with Balakrishnan-Taylor term is considered. At
first, a local existence is established by the linear approximation together with the Faedo-
Galerkin method. Then, by establishing several reasonable conditions and suitable energy
inequalities, the solution of the problem admits a general decay in time.