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Discontinuity, Nonlinearity, and Complexity 11(2) (2022) 275--284 | DOI:10.5890/DNC.2022.06.007

Tebba Zakia$^{1}$, Hakima Degaichia$^{2}$, Hadia Messaoudene$^{3}$

$^{1}$ Laboratory of Mathematics, Informatics and Systems, Larbi Tebessi, University, Tebessa, Algeria

$^{2}$ Department of Mathematics and Computer Science, Larbi Tebessi, University, Tebessa, Algeria

$^{3}$ Faculty of Economics Sciences and Management, Larbi Tebessi, University, Tebessa, Algeria

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Abstract

A new class of nonlinear viscoelastic wave equation is studied. Under appropriate conditions imposed on h, the global existence of solutions with any initial data is proved when $m\geq p$, and a finite time blow-up with negative initial energy is obtained when $p>m$.

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