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Abstract
In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.
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1 Amar Teleji Laghouat University, Department of Material Sciences, Faculty of Sciences, Laghouat, Algeria (GRID:grid.440472.1); Ghardaia University, Laboratory of Mathematics and Applied Sciences, Ghardaia, Algeria (GRID:grid.442442.0) (ISNI:0000 0004 1786 1341)
2 Badji Mokhtar-Annaba University, Department of Mathematics, Faculty of Sciences, Annaba, Algeria (GRID:grid.440473.0) (ISNI:0000 0004 0410 1298)
3 Qassim University, Department of Mathematics, College of Science, Buraydah, Saudi Arabia (GRID:grid.412602.3) (ISNI:0000 0000 9421 8094)