On determination of the source term of a modified KdV equation

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:

Inverse Problem, KdV Equation, Source Term Identification, Overdetermination Condition Operator Equation,

PDF

___

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. N. A. Larkin. Korteweg-de Vries and Kuramoto-Sivashinsky equation in bounded domains. Journal of Mathematical Analysis and Applications 297 (2004) 169-185.
3. M. Tsutsumi. On global solutions of the modified KdV equation in inhomogeneous media. Funkcialaj Ekvacioj 15 (1972) 161-172.
4. H. Cai. Dispersive smoothing efects for KdV type equations. Journal of Differential Equations 136 (1997) 191-221.
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. 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. 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. V. Isakov. Inverse Source Problems. Mathematical Surveys and Monographs. Vol. 34, American Mathematical Society, Providence,RI, 1990.
9. I. B. Bereznits'ka. Inverse problems of determination of the source term in a general parabolic equation. Mat. Stud. 18 (2) (2002) 169- 176.
10. O. V. Drozhzhina. The inverse problem for numerical determination of the nonlinear right-hand side in a parabolic equation. Computational Mathematics and Modeling, 14 (4) (2003) 350-359.
11. A. I. Kozhanov. On the solvability of an inverse problem with unknown coefficient and right-hand side for a parabolic equation. Journal of Inverse Ill-Posed Problems, 10(6) (2002), 611-629.
12. S. Kesevan. Topics in Functional Analysis and Applications. John Wiley and Sons, Newyork, Chichester, Brisbane, Toronto, Singapore, 1989.
13. E. Zeidler. Nonlinear Functional Analysis and its Applications. Springer-Verlag, Newyork, Berlin, Heidelberg, Tokyo, 1986