Two stability results for the Kawahara equation with a time-delayed boundary control

Roberto de A. Capistrano-Filho, Boumediène Chentouf*, Luan S. de Sousa, Victor H. Gonzalez Martinez

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةArticleمراجعة النظراء

3 اقتباسات (Scopus)


In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the length of the spatial domain. Specifically, the first result is obtained by introducing a suitable energy functional and using Lyapunov’s approach, to ensure that the energy of the Kawahara system goes to 0 exponentially as t→ ∞. The second result is achieved by employing a compactness–uniqueness argument, which reduces our study to prove an observability inequality. Furthermore, the novelty of this work is to characterize the critical lengths phenomenon for this equation by showing that the stability results hold whenever the spatial length is related to the Möbius transformations.

اللغة الأصليةEnglish
رقم المقال16
دوريةZeitschrift fur Angewandte Mathematik und Physik
مستوى الصوت74
رقم الإصدار1
المعرِّفات الرقمية للأشياء
حالة النشرPublished - فبراير 2023

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