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Analytical solutions of a class of inverse coefficient problems. (English) Zbl 1251.35190
Summary: This paper is devoted to some class of inverse coefficient problems. By using a well-known transformation, the inverse problem is transformed to a new problem without the unknown time dependent coefficient. Therefore, the new inverse problem can be solved easily. To show the efficiency of the present method, some examples are presented.
35R30Inverse problems for PDE
35A22Transform methods (PDE)
35K10Second order parabolic equations, general
35Q93PDEs in connection with control and optimization
Full Text: DOI
[1] Cannon, J. R.; Lin, Y.; Wang, S.: Determination of parameter $p(t)$ in some quasi-linear parabolic differential equations, Inverse problems, 35-45 (1998) · Zbl 0697.35162 · doi:10.1088/0266-5611/4/1/006
[2] Canon, J. R.; Tatari, M.: Identifying an unknown function in a parabolic equation with overspecifed data via he’s variational iteration method, Chaos solitons fractals, 157-166 (2008) · Zbl 1152.35390 · doi:10.1016/j.chaos.2006.06.023
[3] Dehghan, M.; Tatari, M.: He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation, Chaos solitons fractals, 671-677 (2007) · Zbl 1131.65084 · doi:10.1016/j.chaos.2006.01.059
[4] Liu, J. B.; Tang, J.: Variational iteration method for solving an inverse parabolic equation, Phys. lett. A 372, 3569-3572 (2008) · Zbl 1220.35004 · doi:10.1016/j.physleta.2008.02.042
[5] Ou, Y. H.; Zhao, J.; Liu, Z. H.; Tang, J.: Determination of the unknown time dependent coefficient $p(t)$ in the parabolic equation ut=?$u+p(t)u+\phi $(x,t), J. inverse ill-posed probl. 19, 525-531 (2011) · Zbl 1279.35061
[6] He, J. H.: Variational iteration method--a kind of non-linear analytical technique: some examples, Internat. J. Non-linear mech. 34, 699-708 (1999) · Zbl 05137891
[7] He, J. H.: Variational iteration method-some recent results and new interpretations, J. comput. Appl. math. 207, 3-17 (2007) · Zbl 1119.65049 · doi:10.1016/j.cam.2006.07.009
[8] He, J. H.; Wu, X. H.: Variational iteration method: new development and applications, J. comput. Appl. math. 54, 881-894 (2007) · Zbl 1141.65372 · doi:10.1016/j.camwa.2006.12.083
[9] Odibat, Zaid M.: A study on the convergence of variational iteration method, Math. comput. Modelling 51, 1181-1192 (2010) · Zbl 1198.65147 · doi:10.1016/j.mcm.2009.12.034
[10] Macbain, J. A.; Bednar, J. B.: Existence and uniqueness properties for one-dimensional magnetotelluric inversion problem, J. math. Phys. 27, 645-649 (1986)
[11] Prilepko, A. I.; Soloev, V. V.: Solvability of the inverse boundary value problem of finding a coefficient of a lower order term in a parabolic equation, J. differential equations 32, 136-143 (1987)
[12] Hasanov, A.; Liu, Z.: An inverse coefficient problem for a nonlinear parabolic variational inequality, Appl. math. Lett., 563-570 (2008) · Zbl 1143.35385 · doi:10.1016/j.aml.2007.06.007