Global existence and decay for a system of two singular one-dimensional nonlinear viscoelastic equations with general source terms

New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

“…In this subsection, we state, without proof, the local and global existence results for system (1), which can be proved similarly to the ones in [14,18] and [21].…”

“…They proved the global existence and established a decay rate of solution and also a finite time blow up. Recently, Boulaaras et al [21] treated problem (1) and proved the existence of a global solution to the problem using the potential-well theory. Moreover, they established a general decay result in which the relaxation functions k 1 and k 2 satisfy…”

“…Motivated by the above work, we prove a general stability result of system (1) replacing the condition (6) used in [21] by a more general assumption of the form:…”

Blow up of solutions of two singular nonlinear viscoelastic equations with general source and localized frictional damping terms

“…and Q = (0, L) × (0, T), L < ∞, T < ∞, μ ∈ C 1 ((0, L)), g 1 (2). The problems related with localized frictional damping have been extensively studied by many teams [5], where the authors obtained an exponential rate of decay for the solution © The Author(s) 2020.…”

“…Very recently, in [2] we have studied the following singular one-dimensional nonlinear equations that arise in generalized viscoelasticity with long-term memory:…”