Well-posedness and global attractor of Kirchhoff equation with memory term and thermal effect

Abstract The Kirchhoff equation with thermal effect and memory term is studied. The existence and uniqueness of the solution of the equation are obtained by using the Faedo-Galerkin method. Secondly, the existence of global attractor is obtained by proving the existence of bounded absorption set and the asymptotic smoothness of semigroup. For the first time, this paper comprehensively considers the long-term dynamic behavior of the Kirchhoff model under the simultaneous action of variable coefficients, memory and thermal effects, and promotes the relevant conclusions of the Kirchhoff model. The conclusion of this paper provides a theoretical basis for the subsequent research.