General decay for a class of viscoelastic problem with not necessarily decreasing kernel

General decay for Kirchhoff type in viscoelasticity with not necessarily decreasing kernel

“…Recently, in Ouchenane et al, the authors have improved the earlier result in Mesloub and Boulaaras and Medjden and Tatar where only the exponential rate was considered. In this situation, we have discussed the general decay result for the solution of a class of coupled viscoelastic system with not necessarily decreasing kernel.…”

“…A viscoelastic material will return to its original shape after any deforming force has been removed even though it will take time to do; see previous studies and Zennir . In recent years, problems involving viscoelasticity have been studied in many papers, and several results concerning the global existence and decay of global solution have been established, where the relaxation function was assumed to be either of exponential or of polynomial decay.…”

“…In this situation, we have discussed the general decay result for the solution of a class of coupled viscoelastic system with not necessarily decreasing kernel. In this current work, we follow up the same steps of previous result in Ouchenane et al for a class of Kirrchoff hyperbolic equation in bounded domains, which is defined in with respect to the same conditions in the previous ones.…”

General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity

“…Viscoelasticity and related phenomena are interested in the biological materials study. A viscoelastic material will return to its original shape after any deforming force has been removed even though it will take time to do so (see previous studies). In the absence of the Balakrishnan‐Taylor damping in our problem , ie, σ =0, problem has been extensively studied, and several results concerning existence, nonexistence, and asymptotic behavior have been established (see, eg, Nakao, Ono, and Li and Tsai for the case h ( t )=0 and Cavalcanti et al for the case ξ 1 =0 ).…”

Polynomial Decay Rate for Kirchhoff Type in Viscoelasticity with Logarithmic Nonlinearity and Not Necessarily Decreasing Kernel

“…Viscoelasticity has an important role in the study of biological phenomena, and it can have a strong effect on some factors that have a correlation with biological phenomenain general. A viscoelastic material will return back to its original size after an influential force has been detached, even though it will remain for a specific time in its original shape; see [1][2][3][4][5][6][7][8][9][10][11].…”