IJMNTA  Vol.6 No.1 , March 2017
On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation
Abstract: In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.
Cite this paper: Lin, G. , Gao, Y. and Sun, Y. (2017) On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation. International Journal of Modern Nonlinear Theory and Application, 6, 11-25. doi: 10.4236/ijmnta.2017.61002.

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