Recovering a Time-Dependent Diffusion Coefficient from Nonlocal Data

С. И. Кабанихин1,2,3, Maxim Shishlenin1,2,3
1Sobolev Institute of Mathematics, Novosibirsk, Russia
2Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
3Novosibirsk State University, Novosibirsk, Russia

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Vabishchevich, P.N. and Klibanov, M.V., Numerical Identification of the Leading Coefficient of a Parabolic Equation, Diff. Ur., 2016, vol. 52, no. 7, pp. 896–903.

Gubaydullin, I.M., Zhalnin, R.V., Masyagin, V.F., Tishkin, V.F., and Shurshina, A.S., Application of the DG Method for Solving Inverse Problem of Medicine Diffusion from the Chitosan Film, SVMO Zh., 2016, vol. 18, no. 2, pp. 94–105.

Bouziani, A., Mixed Problem with Integral Conditions for a Certain Parabolic Equation, J. Appl. Math. Stoch. An., 1996, vol. 9, pp. 323–330.

Cannon, J.R. and Rundell, W., Recovering a Time-DependentCoefficient in a Parabolic Differential Equation, J. Math. An. Appl., 1991, vol. 160, pp. 572–582.

Cannon, J.R. and Yin, H.-M., Numerical Solutions of Some Parabolic Inverse Problems, Num. Meth. Part. Diff. Eq., 1990, vol. 6, pp. 177–191.

Dehghan, M., Identification of a Time-Dependent Coefficient in a Partial Differential Equation Subject to an ExtraMeasurement, Nume. Meth. Part. Diff. Eq., 2005, vol. 21, pp. 611–622.

Ivanchov, N.I., On the Determination of the Time-Dependent Leading Coefficient in a Parabolic Equation, Sib.Mat. Zh., 1998, vol. 39, pp. 539–550.

Hussein, M., Lesnic, D., and Ismailov, M.I., An Inverse Problem of Finding the Time-Dependent Diffusion Coefficient from an Integral Condition, Math. Meth. Appl. Sci., 2016, vol. 39, no. 5, pp. 963–980.

Liao, W., Dehghan M. and Mohebbi, A., Direct Numerical Method for an Inverse Problem of a Parabolic Partial Differential Equation, J. Comput. Appl.Math., 2009, vol. 232, pp. 351–360.

Onyejekwe, O.N., Determination of Two Time-Dependent Coefficients in a Parabolic Partial Differential Equation by Homotopy Analysis Method, Int. J. Appl. Math. Res., 2014, vol. 3, no. 2, pp. 161–167.

Shaik, M. R., Korsapati, M., and Panati, D., Polymers in Controlled Drug Delivery Systems, Int. J. Pharm. Sei., 2012, vol. 2, no. 4, pp. 112–116.

Vilar, G., Tulla-Puche, J., and Albericio, F., Polymers and Drug Delivery Systems, Current Drug Delivery, 2012, vol. 9, no. 4, pp. 367–394.

Kabanikhin, S.I., Scherzer, O., and Shishlenin, M.A., Iteration Methods for Solving a Two-Dimensional Inverse Problem for a Hyperbolic Equation, J. Inv. Ill-Pos. Probl., 2003, vol. 11, no. 1, pp. 87–109.

Kabanikhin, S.I. and Shishlenin, M.A., Quasi-Solution in Inverse Coefficient Problems, J. Inv. Ill-Pos. Probl., 2008, vol. 16, no. 7, pp. 705–713.

Kabanikhin, S.I. and Shishlenin, M.A., On the Use of a Priori Information in Coefficient Inverse Problems for Hyperbolic Equations, Proc. Krasovskii Inst. Math. Mech. UB RAS, 2012, vol. 18, no. 1, pp. 147–164.

Kabanikhin, S.I., Definitions and Examples of Inverse and Ill-Posed Problems, J. Inv. Ill-Pos. Probl., 2008, vol. 16, no. 4, pp. 317–357.

Alifanov, O.M., Inverse Heat Transfer Problems, Springer-Verlag, 2011.