Abstract
This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$
k
i
, namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$
k
i
′
(
t
)
≤
−
ξ
i
(
t
)
Ψ
i
(
k
i
(
t
)
)
,
i
=
1
,
2
.
We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$
k
i
(
s
)
=
s
p
and p covers the full admissible range $[1, 2)$
[
1
,
2
)
.
Blow up of solutions for a system of two singular nonlocal viscoelastic equations with damping, general source terms and a wide class of relaxation functions