        TY  - JOUR
T1  - Decay Estimate for the Time-Delayed Fourth-Order Wave Equations
AU  - Meyvacı, Müge
PY  - 2021
DA  - September
Y2  - 2021
DO  - 10.36753/mathenot.777927
JF  - Mathematical Sciences and Applications E-Notes
JO  - Math. Sci. Appl. E-Notes
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2147-6268
SP  - 142
EP  - 150
VL  - 9
IS  - 3
LA  - en
AB  - The objective of this article is to analyze the stability of solutions for the following fourth- order nonlinear wave equations with an internal delay term:\begin{equation*}u_{tt} + \Delta^2 u + u + \sigma_1(t) |u_{t}(x,t)|^{2m-2} u_t(x,t) + \sigma_2(t) |u_{t} (x,t-\tau)|^{2m-2} u_t(x,t-\tau) = 0.\end{equation*}We obtain appropriate conditions on $\sigma_1(t)$ and $\sigma_2(t)$ for the decay properties of the solutions. The multiplier technique and nonlinear integral inequalities are used in the proof.
KW  - fourth order wave
KW  - asymptotic behavior
KW  - energy decay rate
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UR  - https://doi.org/10.36753/mathenot.777927
L1  - https://dergipark.org.tr/en/download/article-file/1230856
ER  -