تقرير
On the boundary stabilization of the KdV-KdV system with time-dependent delay
| العنوان: | On the boundary stabilization of the KdV-KdV system with time-dependent delay |
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| المؤلفون: | Capistrano-Filho, Roberto de A., Chentouf, Boumediène, Martinez, Victor H. Gonzalez, Muñoz, Juan Ricardo |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35Q53, 93D15, 93C20, 93D30 |
| الوصف: | The boundary stabilization problem of the Boussinesq KdV-KdV type system is investigated in this paper. An appropriate boundary feedback law consisting of a linear combination of a damping mechanism and a delay term is designed. Then, first, considering time-varying delay feedback together with a smallness restriction on the length of the spatial domain and the initial data, we show that the problem under consideration is well-posed. The proof combines Kato's approach and the fixed-point argument. Last but not least, we prove that the energy of the linearized KdV-KdV system decays exponentially by employing the Lyapunov method. Comment: To appear Nonlinear Analysis: Real World Applications |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.nonrwa2024.104122 |
| URL الوصول: | http://arxiv.org/abs/2305.15532 |
| رقم الأكسشن: | edsarx.2305.15532 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.nonrwa2024.104122 |
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