INERTIAL MANIFOLD FAMILY OF HIGH-ORDER NONLINEAR KIRCHHOFF-TYPE EQUATION
In this paper, we study a finite-dimensional Lipschitz inertial manifold family of a class of high-order nonlinear Kirchhoff-type equations. First, the high-order Kirchhoff-type equation is transformed into a first-order evolution equation, the graph norm in X = Ek is defined, and the operator A is proved to be non-negative. Then we prove the Lipschitz continuity of the nonlinear term. We verify that the operator A satisfies the spectral interval condition. Finally, the existence of an inertial manifold family in the space X is established.
Kirchhoff-type equation, inertial manifold family, spectral interval condition, Lipschitz continuity.