TY - JOUR
T1 - Well-posedness and stability of a nonlinear time-delayed dispersive equation via the fixed point technique
T2 - A case study of no interior damping
AU - Ammari, Kaïs
AU - Chentouf, Boumediène
AU - Smaoui, Nejib
N1 - Funding Information:
This work was supported and funded by Kuwait University, Research Grant SM05/18. The authors are grateful to the editor and the two anonymous referees for their careful reading of the first version of the manuscript and for their insightful comments and constructive suggestions.
Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.
PY - 2022
Y1 - 2022
N2 - The primary concern of this article is to establish the well-posedness as well as the exponential stability of the zero solution to a nonlinear time-delayed dispersive equation of order four in a bounded interval. The main ingredient of the proof is the exploitation of Schauder Fixed Point Theorem. This outcome considerably improves an earlier result of Ammari et al. (2021) in the sense that we prove that no interior damping control is required. Furthermore, our results remain valid regardless of the sign of the antidiffusion parameter. Numerical simulations are also given as an illustration of our theoretical result.
AB - The primary concern of this article is to establish the well-posedness as well as the exponential stability of the zero solution to a nonlinear time-delayed dispersive equation of order four in a bounded interval. The main ingredient of the proof is the exploitation of Schauder Fixed Point Theorem. This outcome considerably improves an earlier result of Ammari et al. (2021) in the sense that we prove that no interior damping control is required. Furthermore, our results remain valid regardless of the sign of the antidiffusion parameter. Numerical simulations are also given as an illustration of our theoretical result.
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U2 - 10.1002/mma.8052
DO - 10.1002/mma.8052
M3 - Article
AN - SCOPUS:85122303509
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
ER -