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A New Algorithm for Determining the Leading Coefficient of in the Parabolic Equation
Abstract:This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327447Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1257
 M.I.Ivanchov, Inverse problem of heat condition with nonlocal conditions, Dop.Nats.Akad.Nauk Ukrainy,NO.5,15-21, 1997
 A.I.Prilepko and A.B. Kostin, On inverse problems of determination of a coefficients in a parabolic equation, I, Sib. Mat. Zh.33,No.3, 146- 155(1992)
 Akhundov A. Ya., An inverse problem for linear parabolic equations, Dokl. Akad. Nauk AzSSR, 39, No. 5, 3-6 (1983).
 Ivanchov N. I., On the inverse problem of simultaneous determination of thermal conductivity and specific heat capacity, Sibirsk. Mat. Zh., 35, No. 3, 612-621 (1994).
 N.I.Ivanchov and N. V. Pabyrivska, On determination of two timedependent coefficients in a parabolic equation, Siberian Mathematical Journal, Vol. 43, No. 2, pp. 323-329, 2002
 I. B. Bereznyts-ka, Determination of the free term and leading coefficient in a parabolic equation, Ukrainian Mathematical Journal, Vol. 55, No. 1, 2003
 Y.M.Chen, Generalized Pulse-Spectrum Technique, Geophysics, 50(1985)1664-1675
 B.Han, M.L.Zhang, and J,Q.Liu, A widely convergent Genevalized Pulse- Spectrum Technique for the coefficient converse problem of Differential equations, Applied Mathematics and Computation, 81(1997)97-112 12
 A.B.Bakushinsky, A.V.Goncharsky, Ill-posed problem:Theory and Applications, Kluwer Academic, Dordrecht,1994
 A.N.Tikhonov,A.S.Leonov,A.G.Yagola, Nonlinear Ill-posed Problems, Chapman and Hall, London, 1998
 M.V.Klibanov, A.Timonov, A new slant on the inverse problems of electromagnetic frequency sounding:-convexification- of a multiextremal objective function via the CarlemanWeight functions, Inverse Problem,17(2001)1865-1887
 M.V.Klibanov, A.Timonov, A globally convergent convexification algorithm for the inverse problem of electromagnetic frequency sounding in one dimension, Numer. Methods Programming, 4(2003)52-81
 N. Aronszajn, Theory of reproducing kernels, Trans. A.M.S.,68,1950:337-404
 Zhong Chen, YingZhen Lin, The exact solution of a linear integral equation with weakly singular kernel, J. Math. Anal. Appl. 344:726- 734(2008).
 MingGen Cui, Yingzhen Lin, Nonlinear numercial Analysis in the Reproducing kernel space, Nova Science Publisher, New York, 2008.