Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping

Boumediène Chentouf

doi:10.1002/mma.8369

Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping

Boumediène Chentouf^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Journal	Mathematical Methods in the Applied Sciences
DOIs	https://doi.org/10.1002/mma.8369
Publication status	Accepted/In press - 2022
Externally published	Yes

Keywords

exponential stability
localized damping
nonlinear Kawahara equation
time-delay

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/mma.8369

Cite this

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title = "Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping",

abstract = "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.",

keywords = "exponential stability, localized damping, nonlinear Kawahara equation, time-delay",

author = "Boumedi{\`e}ne Chentouf",

note = "Publisher Copyright: {\textcopyright} 2022 John Wiley & Sons, Ltd.",

year = "2022",

doi = "10.1002/mma.8369",

language = "English",

journal = "Mathematical Methods in the Applied Sciences",

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T1 - Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping

AU - Chentouf, Boumediène

PY - 2022

Y1 - 2022

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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DO - 10.1002/mma.8369

M3 - Article

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SN - 0170-4214

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

ER -

Well-posedness and exponential stability of the Kawahara equation with a time-delayed localized damping

Abstract

Keywords

ASJC Scopus subject areas

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