TY - JOUR
T1 - Well-posedness and exponential stability results for a nonlinear Kuramoto-Sivashinsky equation with a boundary time-delay
AU - Chentouf, Boumediène
N1 - Funding Information:
The author is grateful to the editor for handling the paper and to the anonymous referee for the careful reading of the original manuscript. His/her valuable remarks and comments have led to an improved version of the article.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/12
Y1 - 2021/12
N2 - The main concern of this article is to deal with the presence of a boundary delay in the nonlinear Kuramoto-Sivashinsky equation. First, we prove that the whole system is well-posed under a smallness assumption on the initial data and a condition on the parameter involved in the delay term. Then, the solution is shown to decay exponentially despite the presence of the delay. These findings are proved by considering several situations depending on the physical parameters of the system.
AB - The main concern of this article is to deal with the presence of a boundary delay in the nonlinear Kuramoto-Sivashinsky equation. First, we prove that the whole system is well-posed under a smallness assumption on the initial data and a condition on the parameter involved in the delay term. Then, the solution is shown to decay exponentially despite the presence of the delay. These findings are proved by considering several situations depending on the physical parameters of the system.
KW - Boundary delay
KW - Exponential Stability
KW - Nonlinear Kuramoto-Sivashinsky equation
KW - Well-posedness
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U2 - 10.1007/s13324-021-00578-1
DO - 10.1007/s13324-021-00578-1
M3 - Article
AN - SCOPUS:85111481072
SN - 1664-2368
VL - 11
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 4
M1 - 144
ER -