%0 Journal Article
%T On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation
%A Guoguang Lin
%A Yunlong Gao
%A Yuting Sun
%J International Journal of Modern Nonlinear Theory and Application
%P 11-25
%@ 2167-9487
%D 2017
%I Scientific Research Publishing
%R 10.4236/ijmnta.2017.61002
%X In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: <img src=\"Edit_86ac04b7-1d30-4853-9831-174f885fd50e.bmp\" alt=\"\" />. At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by ˇ°Concavityˇ± method we establish three blow-up results for certain solutions in the case 1): <img src=\"Edit_c22cc375-aa71-4d62-8d82-07b607f1cb01.bmp\" alt=\"\" />, in the case 2): <img src=\"Edit_4dc08937-4b56-4f0c-a0dd-1e18512f0079.bmp\" alt=\"\" /> and in the case 3): <img src=\"Edit_e492d220-1c50-47ac-a0d4-3641f16c2c1f.bmp\" alt=\"\" />. At last, we consider that the estimation of the upper bounds of the blow-up time <img src=\"Edit_3fd39c42-ae7d-490e-a5ec-a631435c08ea.bmp\" alt=\"\" />is given for deferent initial energy.
%K Nonlinear Higher-Order Kirchhoff Type Equation
%K Strong Damping
%K Local Solutions
%K Blow-Up
%K Initial Energy
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=74071