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The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Linear Damping
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
- 1 Department of Mathematics, Yunnan University, Kunming, China
- 2 Department of Mathematics, Yunnan University, Kunming, China
- 3 Department of Mathematics, Yunnan University, Kunming, China
International Journal of Modern Nonlinear Theory and Application·Volume 05 (2016)·Pages 185–202·Published 10 November 2016·DOI10.4236/ijmnta.2016.54018
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Abstract
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
KeywordsNonlinear Higher-Order Kirchhoff Type EquationThe Existence and UniquenessThe Global AttractorsHausdorff DimensionsFractal Dimensions
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