Qualitative Analysis of the Dynamic for the Nonlinear Korteweg–de Vries Equation with a Boundary Memory

Boumediène Chentouf*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمراجعة النظراء

6 اقتباسات (Scopus)

ملخص

This paper addresses the impact of the presence of a boundary memory term in the third-order Korteweg–de Vries equation in a bounded interval [0 , ℓ]. First, an overall literature review is provided. Indeed, a comprehensive discussion on the literature constitutes a survey part of the current paper. Thereafter, it is shown that the system under consideration possesses a unique solution under a smallness assumption on the initial data and an appropriate condition on the parameters and the kernel involved in the memory term. Last but not least, we demonstrate that the zero solution is exponentially stable as long as the length ℓ is small enough by means of Lyapunov method, which permits to provide an estimate of the exponential decay rate. These findings improve and complement those of Zhang (in: Desch W, Kappel F, Kunisch K (eds) Proceedings of international conference on control and estimation of distributed parameter systems: nonlinear phenomena, International Series of Numerical Mathematics, vol 118, Birkhauser, Basel, pp 371–389, 1994) (resp. Baudouin et al. in IEEE Trans Autom Control 64:1403–1414, 2019), where no memory term is present (resp. a delay occurs instead of memory).

اللغة الأصليةEnglish
رقم المقال36
دوريةQualitative Theory of Dynamical Systems
مستوى الصوت20
رقم الإصدار2
المعرِّفات الرقمية للأشياء
حالة النشرPublished - يوليو 2021
منشور خارجيًانعم

ASJC Scopus subject areas

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