Asymptotic Stability for a Viscoelastic Equation with Nonlinear Damping and Very General Type of Relaxation Functions

New general decay results in an infinite memory viscoelastic problem with nonlinear damping

“…In the present work, we study the asymptotic behavior of solutions of (1), under assumption (9) (below) instead of (6) considered in Guesmia [17] and Al-Gharabli [22]. This work will extend the result of Belhannache et al [23] for the finite history case to the infinite history case. The proof of the current result is easier than the one in [17] and [22] since we need no convex function properties or the generalized Young inequality.…”

Optimal decay for second‐order abstract viscoelastic equation in Hilbert spaces with infinite memory and time delay

“…Multiplying the first equation of (6) by u t . Then, repeating exactly the same arguments to obtain (16) and using (10), we get (29).…”

“…For some works used (5), we refer to read previous studies. [14][15][16][17][18][19] Time delays arises in many applications and practical problems and in many cases, even small delay may destabilize a system which is asymptotically stable in the absence of delay, in this sense, see other works. [20][21][22] A large part in the literature is available addressing the stability, instability, and the connection between the memory term, the frictional damping, and the delay terms.…”

Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory

“…This depends on the damping term, the memory term, the relaxation function, and the differential operator. In the presence of memory, the main common challenge was showing the energy decaying for most general relaxation function g, we refer the readers to [1][2][3]6,7,[9][10][11]13].…”