The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations

In this paper, we study the long-time behavior of a class generalized nonlinear Kichhoff equation under condition n dimension. Firstly, Lipschitz property and squeezing semigroup related to initial-boundary value problem are proved, then existence its exponential attractor is obtained. By extending space E0 Ek, family attractors second part, consider for system Kirchhoff type with strong damping terms. Using Hadamard graph transformation method, obtain inertial manifolds while such equations satisfy spectrum interval condition.