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

Abstract

The Kirchhoff model is derived from the vibration problem of stretchable strings. In this paper, the Kirchhoff equation with thermal effects and memory terms is studied. First, the existence and uniqueness of the solution to the equation are obtained using the Faedo–Galerkin method. Then, the existence of a global attractor is established by proving the existence of a bounded absorbing set and the asymptotic smoothness of the semigroup. This paper innovatively considers the long-term dynamic behavior of the Kirchhoff model under the simultaneous action of variable coefficients, memory, and thermal effects comprehensively. It also promotes the relevant conclusions of the Kirchhoff model. The findings of this paper provide a theoretical basis for subsequent application and research.