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\begin{document}

\title{Nonexistence of global solutions to wave Equations with structural
damping and nonlinear memory}



\author[1]{Mokhtar Kirane}%
\author[2]{Abderrazak NABTi}%
\author[3]{Mohamed Jleli}%
\affil[1]{University de La Rochelle}%
\affil[2]{Universite de Tebessa}%
\affil[3]{kING SAUD UNIVERSITY Riyadh, Saudi Arabia}%


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  \date{May 22, 2024}


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\begin{abstract}
For the following wave equations with structural damping and nonlinear
memory source terms \textbackslash{}{[}
u\_\{tt\}+(-\textbackslash{}Delta)\^{}\{\textbackslash{}frac\{\textbackslash{}alpha\}\{2\}\}u
+(-\textbackslash{}Delta)\^{}\{\textbackslash{}frac\{\textbackslash{}beta\}\{2\}\}u\_t
=\textbackslash{}int\_\{0\}\^{}\{t\}(t-s)\^{}\{\textbackslash{}gamma-1\}
\textbackslash{}vert u
(s)\textbackslash{}vert\^{}\{p\}\textbackslash{},\textbackslash{}text\{d\}s,
\textbackslash{}{]} and \textbackslash{}{[}
u\_\{tt\}+(-\textbackslash{}Delta)\^{}\{\textbackslash{}frac\{\textbackslash{}alpha\}\{2\}\}u
+(-\textbackslash{}Delta)\^{}\{\textbackslash{}frac\{\textbackslash{}beta\}\{2\}\}u\_t
=
\textbackslash{}int\_\{0\}\^{}\{t\}(t-s)\^{}\{\textbackslash{}gamma-1\}
\textbackslash{}vert u\_s
(s)\textbackslash{}vert\^{}\{p\}\textbackslash{},\textbackslash{}text\{d\}s,
\textbackslash{}{]} posed in \$(x,t) \textbackslash{}in
\textbackslash{}mathbb\{R\}\^{}N \textbackslash{}times
{[}0,\textbackslash{}infty) \$, where \$u=u(x,t)\$ is real-value unknown
function, \$p\textgreater{}1\$,
\$\textbackslash{}alpha,\textbackslash{}beta\textbackslash{}in (0,
2{]}\$, \$\textbackslash{}gamma\textbackslash{}in (0,1)\$, we prove the
nonexistence of global solutions. Moreover, we give an upper bound
estimate of the life span of solutions.%
\end{abstract}%



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