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.
|Journal||Mathematical Methods in the Applied Sciences|
|Publication status||Accepted/In press - 2022|
- exponential stability
- localized damping
- nonlinear Kawahara equation
ASJC Scopus subject areas