Well-posedness, asymptotic stability and blow-up results for a nonlocal singular viscoelastic problem with logarithmic nonlinearity
Considered herein is the well-posedness, asymptotic stability and blow-up of the initial-boundary value problem for nonlocal singular viscoelastic wave equation with logarithmic nonlinearity u tt - 1 x ( x u x ) x - 1 x ( x u xt ) x + ∫ 0 t m ( t - λ ) 1 x ( x u x ( x , λ ) ) x d λ = | u | r - 2 u l...
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Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2024-04, Vol.75 (2), Article 34 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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Zusammenfassung: | Considered herein is the well-posedness, asymptotic stability and blow-up of the initial-boundary value problem for nonlocal singular viscoelastic wave equation with logarithmic nonlinearity
u
tt
-
1
x
(
x
u
x
)
x
-
1
x
(
x
u
xt
)
x
+
∫
0
t
m
(
t
-
λ
)
1
x
(
x
u
x
(
x
,
λ
)
)
x
d
λ
=
|
u
|
r
-
2
u
ln
|
u
|
subject to a nonlocal boundary condition. Through the effective combining of Galerkin approximation method, modified potential well theory, perturbed energy method, convexity theory and differential-integral inequality techniques, we firstly demonstrate the global existence and uniqueness of weak solutions in certain weighted Sobolev spaces; Secondly, we establish the explicit polynomial and exponential energy decay estimates under some suitable conditions; Finally, we investigate the finite time blow-up criterion and then derive its upper and lower bounds of blow-up time. The above conclusions extend and improve some results in the literatures. |
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ISSN: | 0044-2275 1420-9039 |
DOI: | 10.1007/s00033-023-02177-5 |