Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 4 2023 04 01 Local well-posedness and blow-up of solution for a higher-order wave equation with viscoelastic term and variable-exponent 111 124 7449 10.22075/ijnaa.2023.29383.4149 EN Boughamsa Wissem Department of Mathematics, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria Ouaoua Amar Department of Sciences and Technology, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria Journal Article 2022 12 23 We investigate in this paper a value problem related to the following nonlinear higher-order wave equation $$<br />    \eta_{tt}+\left(  -\Delta\right)  ^{m}\eta-%<br />    %TCIMACRO{\dint \limits_{0}^{t}}%<br />    %BeginExpansion<br />    {\displaystyle\int\limits_{0}^{t}}<br />    %EndExpansion<br />    g\left(  t-s\right)  \left(  -\Delta\right)  ^{m}\eta\left(  s\right)<br />    ds+\eta_{t}=\left\vert \eta\right\vert ^{p\left(  x\right)  -2}\eta.<br />   $$<br />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. https://ijnaa.semnan.ac.ir/article_7449_3c9fba90ebfa6af55af0dfc18fe46738.pdf