A semilinear non-homogeneous problem related to Korteweg-de Vries Equation
DOI:
https://doi.org/10.22199/issn.0717-6279-5825Keywords:
semilinear problem, KdV equation, existence, uniqueness, regularity, anisotropic Sobolev spaceAbstract
In this paper, we consider a non-homogeneous generalized Korteweg-de Vries problem with some hypotheses on the right-hand side, and we give a new regularity result of the solution in an anisotropic Sobolev space. Then we apply the obtained result to a non-homogeneous KdV problem. This work is an extension of solvability results for a right-hand side f in Lebesgue space.
References
E. N. Aksan and A. Ozdes, Numerical solution of Korteweg-de Vries
equation by Galerkin B-spline finite element method, Applied Mathematics and Computation, Vol. 175, No. 2, pp. 1256-1265, 2006. doi.org/10.1016/j.amc.2005.08.038
A. R. Bahadir, Exponential finite difference method applied to
Korteweg-de Vries equation for small times, Appl. Math. Comput.
, 675-682, 2005. doi.org/10.1016/j.amc.2005.08.038
A. Behzadan, M. Holst, Multiplication in Sobolev spaces, revisited.
Available as, 2015. doi.org/10.48550/arXiv.1512.07379
Y. Benia and B. K. Sadallah, Existence of solution to Korteweg-de
Vries equation in domains that can be transformed into rectangles,
Mathematical Methods in the Applied Sciences, Vol. 41, No. 7, pp.
-2698, 2018. doi.org/10.1002/mma.4773
Y. Benia and A. Scapellato, Existence of solution to Korteweg-de Vries
equation in a non-parabolic domain, Nonlinear Analysis, Vol. 195, p.
-12, 2020. doi.org/10.1016/j.na.2020.111758.
Y. Benia, B-K. Sadallah; On the regularity of the solution of nonhomogeneous Burgers equation, Yokohama Mathematical Journal, Vol
(8), pp. 107-124, 2020. DOI: 10.18880/00014022.
T. B. Benjamin, J. L. Bona, J. J. Mahony; Model equations for long
waves in nonlinear dispersive systems. Trans. Roy. Soc. (Lond.) Ser.
A, 272, 47-78, 1992. doi.org/10.1098/rsta.1972.0032
D. G. Crighton Applications of KdV, Acta Applicandae Mathematicae
, 39-67, 1995. doi.org/10.1007/BF00994625.
J. Kevorkian, Partial differential equations: Analytical solution techniques, New York, NY: Chapman amp; Hall, 1996.
J. L. Lions and E. Magenes, Problemes aux limites non homogenes et
applications, Paris: Dunod, 1970. 10.5802/aif.111.
M. He-Ping and G. Ben-Yu, The Fourier pseudospectral method
with a restrain operator for the Korteweg-de Vries equation, Journal of Computational Physics, Vol. 65, No. 1, pp. 120-137, 1986.
doi.org/10.1016/0021-9991(86)90007-0.
S. Zhang, EXP-function method exactly solving a KdV equation with
forcing term, Applied Mathematics and Computation, Vol. 197, No. 1,
pp. 128-134, 2008. doi.org/10.1016/j.amc.2007.07.041.
Published
How to Cite
Issue
Section
Copyright (c) 2024 Yassine Benia
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
