The Dirichlet problem for a wave equation of Kirch-hoff- Carrier type with a nonlinear viscoelastic term

By Ly Anh Duong, Le Huu Ky Son, Le Thi Phuong Ngoc
DOI: 10.37550/tdmu.EJS/2023.05.420

In this paper, we consider the Dirichlet problem for a wave equation of Kirchhoff-
Carrier type with a nonlinear viscoelastic term. It consists of two main parts. In Part
1, we establish existence and uniqueness of a weak solution by applying the Faedo-
Galerkin method and the standard arguments of density corresponding to the regularity
of initial conditions. In Part 2, we give a sufficient condition for the global existence
and exponential decay of the weak solutions by defining a modified energy functional
together with the technique of Lyapunov functional.