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The Inertial Manifold for Class Kirchhoff-Type Equations with Strongly Damped Terms and Source Terms

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Document pages: 8 pages

Abstract: In this paper, we study the inertial manifolds for a class of the Kirchhoff-typeequations with strongly damped terms and source terms. The inertial manifoldis a finite dimensional invariant smooth manifold that contains the globalattractor, attracting the solution orbits by the exponential rate. Under appropriateassumptions, we firstly exert the Hadamard’s graph transformationmethod to structure a graph norm of a Lipschitz continuous function, andthen we prove the existence of the inertial manifold by showing that the spectralgap condition is true.

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