On the radius of spatial analyticity for the higher order nonlinear dispersive equation

Aissa Boukarou; Kaddour Guerbati; Khaled Zennir

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 1, page 19-32
  • ISSN: 0862-7959

Abstract

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In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data u 0 . The analytic initial data can be extended as holomorphic functions in a strip around the x -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).

How to cite

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Boukarou, Aissa, Guerbati, Kaddour, and Zennir, Khaled. "On the radius of spatial analyticity for the higher order nonlinear dispersive equation." Mathematica Bohemica 147.1 (2022): 19-32. <http://eudml.org/doc/297802>.

@article{Boukarou2022,
abstract = {In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_\{0\}$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).},
author = {Boukarou, Aissa, Guerbati, Kaddour, Zennir, Khaled},
journal = {Mathematica Bohemica},
keywords = {higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law},
language = {eng},
number = {1},
pages = {19-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the radius of spatial analyticity for the higher order nonlinear dispersive equation},
url = {http://eudml.org/doc/297802},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Boukarou, Aissa
AU - Guerbati, Kaddour
AU - Zennir, Khaled
TI - On the radius of spatial analyticity for the higher order nonlinear dispersive equation
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 1
SP - 19
EP - 32
AB - In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_{0}$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
LA - eng
KW - higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law
UR - http://eudml.org/doc/297802
ER -

References

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  2. Boukarou, A., Guerbati, K., Zennir, K., Alodhaibi, S., Alkhalaf, S., 10.3390/math8050809, Mathematics 8 (2020), Article ID 809, 16 pages. (2020) DOI10.3390/math8050809
  3. Boukarou, A., Zennir, K., Guerbati, K., Georgiev, S. G., 10.1007/s12215-020-00504-7, Rend. Circ. Mat. Palermo (2) 70 (2021), 349-364. (2021) Zbl1462.35139MR4234317DOI10.1007/s12215-020-00504-7
  4. Boukarou, A., Zennir, K., Guerbati, K., Svetlin, G. G., 10.1007/s11565-020-00340-8, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 66 (2020), 255-272. (2020) MR4156193DOI10.1007/s11565-020-00340-8
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  6. Grujić, Z., Kalisch, H., Local well-posedness of the generalized Korteweg-de Vries equation in spaces of analytic functions, Differ. Integral Equ. 15 (2002), 1325-1334. (2002) Zbl1031.35124MR1920689
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  10. Petronilho, G., Silva, P. L. da, 10.1002/mana.201800394, Math. Nachr. 292 (2019), 2032-2047. (2019) Zbl1427.35220MR4009345DOI10.1002/mana.201800394
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  12. Selberg, S., Tesfahun, A., 10.1016/j.jde.2015.06.007, J. Differ. Equations 259 (2015), 4732-4744. (2015) Zbl1321.35179MR3373420DOI10.1016/j.jde.2015.06.007
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