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Research Article | Open Access

Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation

Aissa Boukarou1, Khaled Zennir2,3( ), Mohamed Bouye4, Abdelkader Moumen5
boukarouaissa@gmail.com]]>
k.zennir@qu.edu.sa]]>
k.zennir@univ-skikda.dz]]>
mbmahmad@kku.edu.sa]]>
mo.abdelkader@uoh.edu.sa]]>
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Abstract

By using linear, bilinear, and trilinear estimates in Bourgain-type spaces and analytic spaces, the local well-posedness of the Cauchy problem for the a Kawahara-Korteweg-de-Vries equation

∂tu+ω∂x5u+ν∂x3u+μ∂xu2+λ∂xu3+d(x)u=0,

was established for analytic initial data u0. Besides, based on the obtained local result, together with an analytic approximate conservation law, we prove that the global solutions exist. Furthermore, the analytic radius has a fixed positive lower bound uniformly for all time.

Keywords

analytic radiusKawahara-Korteweg-de-Vries equationdamped effectnonlinear equations
CLC number: 35G25, 35K55

References

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22414-22434
DOI: 10.3934/math.20241090

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Boukarou A, Zennir K, Bouye M, et al. Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation. AIMS Mathematics, 2024, 9(8): 22414-22434. https://doi.org/10.3934/math.20241090

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Received: 28 May 2024
Revised: 07 July 2024
Accepted: 10 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)