فهرست نشریات علمی دسترسی آزاد ایران

We investigate in this paper a value problem related to the following nonlinear higher-order wave equation $$    \eta_{tt}+\left(  -\Delta\right)  ^{m}\eta-%    %TCIMACRO{\dint \limits_{0}^{t}}%    %BeginExpansion    {\displaystyle\int\limits_{0}^{t}}    %EndExpansion    g\left(  t-s\right)  \left(  -\Delta\right)  ^{m}\eta\left(  s\right)    ds+\eta_{t}=\left\vert \eta\right\vert ^{p\left(  x\right)  -2}\eta.   $$Firstly, we prove the existence and uniqueness of the local solution under suitable conditions for the relaxation function $g$ and viable-exponent $p\left(  .\right)  $, using a method, which is a mixture of the Faedo-Galarkin and Banach fixed point theorem, and prove also the solution blows up in finite time. Finally, we give a two-dimensional numerical example to illustrate the blow-up result.