On the study the radius of analyticity for Korteweg-de-Vries type systems with a weakly damping

Sadok Otmani; Aissa Bouharou; Khaled Zennir; Keltoum Bouhali; Abdelkader Moumen; Mohamed Bouye; Sadok Otmani; Aissa Bouharou; Khaled Zennir; Keltoum Bouhali; Abdelkader Moumen; Mohamed Bouye

doi:10.3934/math.20241375

AIMS Mathematics

2024, Volume 9, Issue 10: 28341-28360. doi: 10.3934/math.20241375

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On the study the radius of analyticity for Korteweg-de-Vries type systems with a weakly damping

1.
Laboratory of Applied Mathematics, Kasdi Merbah University, B. P. 511. 30000 Ouargla, Algeria, Email: sadok.sadok@univ-ouargla.dz
2.
University of Science and Technology Houari Boumediene, Bab Ezzouar, Algeria, Email: boukarouaissa@gmail.com
3.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia, Email: k.zennir@qu.edu.sa, k.bouhali@qu.edu.sa
4.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia, Email: mo.abdelkader@uoh.edu.sa
5.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia, Email: mbmahmad@kku.edu.sa

Received: 29 August 2024 Revised: 24 September 2024 Accepted: 25 September 2024 Published: 30 September 2024
MSC : 35B40, 35L70

In the present paper, we considered a Korteweg-de Vries type system with weakly damping terms and initial data in the analytic Gevery spaces. The presence of tow functions $ c_1(x), c_2(x) $, called damping coefficients, made the system more interesting from an application point of view due to their great importance in physics. To start, by using the fixed point theorem in Banach space, we investigated the local well-posedness. Additionally, by employing an approximate conservation law, we extended this to be global in time, ensuring that the radius of analyticity of solutions remained uniformly bounded below by a fixed positive number for all time.
- KdV system,
- global Well-posedness,
- analytic spaces,
- nonlinear equations,
- approximate conservation law,
- iterative methods
Citation: Sadok Otmani, Aissa Bouharou, Khaled Zennir, Keltoum Bouhali, Abdelkader Moumen, Mohamed Bouye. On the study the radius of analyticity for Korteweg-de-Vries type systems with a weakly damping[J]. AIMS Mathematics, 2024, 9(10): 28341-28360. doi: 10.3934/math.20241375

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Abstract

In the present paper, we considered a Korteweg-de Vries type system with weakly damping terms and initial data in the analytic Gevery spaces. The presence of tow functions $ c_1(x), c_2(x) $, called damping coefficients, made the system more interesting from an application point of view due to their great importance in physics. To start, by using the fixed point theorem in Banach space, we investigated the local well-posedness. Additionally, by employing an approximate conservation law, we extended this to be global in time, ensuring that the radius of analyticity of solutions remained uniformly bounded below by a fixed positive number for all time.

References

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