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 IJMNTA  Vol.7 No.2 , June 2018
The Inertial Manifold for a Class of Nonlinear Higher-Order Coupled Kirchhoff Equations with Strong Linear Damping
Abstract: This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.
Cite this paper: Lin, G. and Hu, L. (2018) The Inertial Manifold for a Class of Nonlinear Higher-Order Coupled Kirchhoff Equations with Strong Linear Damping. International Journal of Modern Nonlinear Theory and Application, 7, 35-47. doi: 10.4236/ijmnta.2018.72003.
References

[1]   Foias, C., Sell, G.R. and Temam, R. (1985) Varietes inertielles des equations differentielles dissipatives. Comptes Rendus de I Academie des Science-Series I-Mathematics, 301, 139-142.

[2]   Constantin, P., Foias, C., Nicolaenko, B. and Temam, R. (1988) Integral and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematical Sciences, Springer-Verlag, New York, 70.

[3]   Fabes, E., Luskin, M. and Sell, G.R. (1991) Construction of Inertial Manifolds by Elliptic Regularization. Journal of Differential Equations, 89, 335-381.
https://doi.org/10.1016/0022-0396(91)90125-S

[4]   Dai, Z.D. and Guo, B.L. (2000) Inertial Manifold and Approximate Inertial Manifold. Science Press, Beijing.

[5]   Wu, J.Z. and Lin, G.G. (2010) Inertial Manifolds for Two-Dimensional Strong Damped Boussinesq Equations. Journal of Yunnan University, 32, 119-124.

[6]   Xu, G.G., Wang, L.B. and Lin, G.G. (2014) Inertial Manifolds for a Class of Nonlinear Time-Delay Wave Equations. Applied Mathematics, 27, 887-891.

[7]   Guo, Y.M. and Li, H.H. (2016) Inertial Manifolds for a Strongly Dissipative Nonlinear Wave Equation. Journal of Anyang Normal University, 5, 62-65.

[8]   Chen, L., Wang, W. and Lin, G.G. (2016) Exponential Attractors and Inertial Manifolds for the Higher-Order Nonlinear Kirchhoff-Type Equation. International Journal of Modern Communication Technologies & Research, 11, 6-12.

[9]   Teman, R. (1988) Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer, New York.

 
 
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