Abstract
This manuscript is concerned with the system
{
u
t
t
=
(
γ
(
Θ
)
u
x
t
)
x
+
(
a
(
x
,
t
)
u
x
)
x
+
(
f
(
Θ
)
)
x
,
Θ
t
=
D
Θ
x
x
+
γ
(
Θ
)
u
x
t
2
+
f
(
Θ
)
u
x
t
,
which is used to describe thermoviscoelastic developments in one-dimensional Kelvin–Voigt materials.
It is assumed that
a
,
γ
and
f
are sufficiently smooth functions that satisfy
c
γ
γ
(
ζ
)
C
γ
,
γ
″
(
ζ
)
≤
0
,
f
(
0
)
=
0
,
|
f
′
(
ζ
)
|
≤
C
f
and
|
f
(
ζ
)
|
≤
C
f
(
1
+
ζ
)
α
for all
ζ
≥
0
and some positive constants
c
γ
,
C
γ
,
C
f
>
0
and
α
∈
(
0
,
5
/
6
)
. Under these conditions, this study then establishes a result on the existence of global classical solutions for sufficiently smooth but arbitrarily large initial data.