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The Global Attractors and Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Damping
School of Mathematics and Statistics, Yunnan University, Kunming, China
School of Mathematics and Statistics, Yunnan University, Kunming, China
- 1 School of Mathematics and Statistics, Yunnan University, Kunming, China
- 2 School of Mathematics and Statistics, Yunnan University, Kunming, China
International Journal of Modern Nonlinear Theory and Application·Volume 09 (2020)·Pages 63–80·Published 4 November 2020·DOI10.4236/ijmnta.2020.94005
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Abstract
The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.
KeywordsNonlinear Higher-Order Kirchhoff Type EquationThe Priori EstimatesThe Galerkin’s MethodThe Global AttractorsDimension Estimation
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