Abstract
In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.
Highlights
This paper mainly deals with existence of inertial manifolds for a class of higher-order coupled Kirchhoff-type equations:( ) utt + M ∇u 2 + ∇v 2 (−∆)m u + β (−∆)m ut + g1 (u, v) = f1 ( x), (1.1)( ) vtt + M ∇u 2 + ∇v 2 (−∆)m v + β (−∆)m vt + g2 (u, v) = f2 ( x), (1.2)u= ( x, 0) u0 ( x),u= t ( x, 0) u1 ( x), x ∈ Ω, (1.3)v= ( x, 0) v0 ( x), vt= ( x, 0) v1 ( x), x ∈ Ω, (1.4) u ∂=Ω ∂iu ∂μ i ∂=Ω
The inertial manifolds are proved by using spectral gap condition
The main result we gained is that the inertial manifolds are established under the proper assumptions of M ( s) and gi (u, v),i = 1, 2
Summary
This paper mainly deals with existence of inertial manifolds for a class of higher-order coupled Kirchhoff-type equations:. Jingzhu Wu and Guoguang Lin [1] studied the following two-dimensional strong damping Boussinesq equation while α > 2 : utt − α∆u= t − ∆u + u2k+1 f ( x, y) , ( x, y) ∈ Ω,. M. Yang squeezing property of the nonlinear semigroup associated with this equation and the existence of exponential attractors and inertial manifolds. We proved the inertial manifolds by using spectral gap condition
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