TY - JOUR
T1 - Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping
AU - Chentouf, Boumediène
N1 - Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.
PY - 2022/11/15
Y1 - 2022/11/15
N2 - The aim of this article is to investigate the well-posedness and stability problems of the so-called Kawahara equation under the presence of an interior localized delayed damping. The system is shown to be well-posed. Furthermore, we prove that the trivial solution is exponentially stable in spite of the delay effect. Specifically, local and semi-global stability results are established according to the properties of the spatial distribution of the delay term.
AB - The aim of this article is to investigate the well-posedness and stability problems of the so-called Kawahara equation under the presence of an interior localized delayed damping. The system is shown to be well-posed. Furthermore, we prove that the trivial solution is exponentially stable in spite of the delay effect. Specifically, local and semi-global stability results are established according to the properties of the spatial distribution of the delay term.
KW - exponential stability
KW - localized damping
KW - nonlinear Kawahara equation
KW - time-delay
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U2 - 10.1002/mma.8369
DO - 10.1002/mma.8369
M3 - Article
AN - SCOPUS:85130223889
SN - 0170-4214
VL - 45
SP - 10312
EP - 10330
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 16
ER -