On determination of the source term of a modified KdV equation

Volume: 5 Number: 3 September 30, 2018
  • Müjdat Kaya
EN

On determination of the source term of a modified KdV equation

Abstract

We study an inverse problem to identify the source term depending on x of a modified KdV equation. In order to recover source term, we define an inverse problem subject to an overdetermination condition. We converted this inverse problem to an operator equation. The existence and uniqueness of this operator equation is investigated

Keywords

References

  1. 1. N. A. Larkin. Modified KdV equation with a source term in a bounded domain. Mathematical Methods In The Applied Science 29 (2006) 751-765.
  2. 2. N. A. Larkin. Korteweg-de Vries and Kuramoto-Sivashinsky equation in bounded domains. Journal of Mathematical Analysis and Applications 297 (2004) 169-185.
  3. 3. M. Tsutsumi. On global solutions of the modified KdV equation in inhomogeneous media. Funkcialaj Ekvacioj 15 (1972) 161-172.
  4. 4. H. Cai. Dispersive smoothing efects for KdV type equations. Journal of Differential Equations 136 (1997) 191-221.
  5. 5. A. I. Prilepko, D. G. Orlovsky, I. A. Vasin. Methods for solving inverse problems in mathematical physics. Monographs and Textbooks in Pure and Applied Mathematics, 231, Marcel Dekker Inc., Newyork, 2000, xiv+709 pp.
  6. 6. M. Kaya. Determination of the unknown source term in a parabolic problem from the measured data at the final time. Applications of Mathematics 59 (2014) 715-728.
  7. 7. M. Kaya. Determination of the unknown Cauchy data in a linear parabolic problem from the measured data at the final time, Mediterranean Journal of Mathematics 10 (2013) 227-239.
  8. 8. V. Isakov. Inverse Source Problems. Mathematical Surveys and Monographs. Vol. 34, American Mathematical Society, Providence,RI, 1990.

Details

Primary Language

English

Subjects

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Journal Section

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Authors

Müjdat Kaya This is me

Publication Date

September 30, 2018

Submission Date

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Acceptance Date

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Published in Issue

Year 2018 Volume: 5 Number: 3

APA
Kaya, M. (2018). On determination of the source term of a modified KdV equation. Hittite Journal of Science and Engineering, 5(3), 175-178. https://doi.org/10.17350/HJSE19030000083
AMA
1.Kaya M. On determination of the source term of a modified KdV equation. Hittite J Sci Eng. 2018;5(3):175-178. doi:10.17350/HJSE19030000083
Chicago
Kaya, Müjdat. 2018. “On Determination of the Source Term of a Modified KdV Equation”. Hittite Journal of Science and Engineering 5 (3): 175-78. https://doi.org/10.17350/HJSE19030000083.
EndNote
Kaya M (September 30, 2018) On determination of the source term of a modified KdV equation. Hittite Journal of Science and Engineering 5 3 175–178.
IEEE
[1]M. Kaya, “On determination of the source term of a modified KdV equation”, Hittite J Sci Eng, vol. 5, no. 3, pp. 175–178, Sept. 2018, doi: 10.17350/HJSE19030000083.
ISNAD
Kaya, Müjdat. “On Determination of the Source Term of a Modified KdV Equation”. Hittite Journal of Science and Engineering 5/3 (September 30, 2018): 175-178. https://doi.org/10.17350/HJSE19030000083.
JAMA
1.Kaya M. On determination of the source term of a modified KdV equation. Hittite J Sci Eng. 2018;5:175–178.
MLA
Kaya, Müjdat. “On Determination of the Source Term of a Modified KdV Equation”. Hittite Journal of Science and Engineering, vol. 5, no. 3, Sept. 2018, pp. 175-8, doi:10.17350/HJSE19030000083.
Vancouver
1.Müjdat Kaya. On determination of the source term of a modified KdV equation. Hittite J Sci Eng. 2018 Sep. 30;5(3):175-8. doi:10.17350/HJSE19030000083

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