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Discontinuity, Nonlinearity, and Complexity 13(4) (2024) 633--651 | DOI:10.5890/DNC.2024.12.005

Omar Alimerina, Tayeb Hadj Kaddour, Ali Hakem

Laboratory LMA, University of Chlef, Algeria

Laboratory ACDE, University of Sidi Belabbes, Algeria

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Abstract

This paper is devoted to the study of Cauchy problem for viscoelastic damped wave models with nonlinear memory on the right-hand side. The main goal is to prove blow-up results for local (in time) energy solutions. The model that we consider is parabolic-like from the point of view of energy decay estimates of the corresponding linear Cauchy problem with a vanishing right-hand side. For this reason, we apply the test function method to prove our results.

Acknowledgments

The authors would like to thank the reviewers for their corrections, remarks and comments.

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