The paper deals with the problem of establishing existence and uniqueness conditions for the solutiontotheinverseproblemforweaklydegeneratetwo-dimensionalanisotropicparabolicequation. Two time-dependent major coefficients are unknown.

Lorenzi A., Paparoni E. Direct and inverse problems in the theory of materials with memory // Rend. Sem. Univ. Padova. – 1992. – 87. – P. 105-138.

Hazanee A., Lesnic D. Determination of a time-dependent coefficient in the bioheat equation // International Journal of Mechanical Sciences. – 2014. – 88. – P. 259-266.

Kaltenbacher B., Klibanov M. An Inverse Problem for a Nonlinear Parabolic Equation with Applications in Population Dynamics and Magnetics // SIAM J. Math. Anal. – 2008. – 39, №6. – P. 1863–1889.

Di Blasio G., Lorenzi A. An Identification Problem in Age-Dependent Population Diffusion //

Numerical Functional Analysis and Optimization. – 2013. – 34, №1. – P. 36-73.

Bouchouev I., Isakov V. The inverse problem of option pricing // Inverse Problems. – 1997. – 13. – P. 7–11.

Kabanikhin S. I. Definitions and examples of inverse and ill-posed problems // J. Inv. Ill-Posed Problems. – 2008. – 16. – P. 317–357.

Lorenzi A., Paparoni E. Direct and inverse problems in the theory of materials with memory // Rend. Sem. Univ. Padova. – 1992. – 87. – P. 105-138.

Hazanee A., Lesnic D. Determination of a time-dependent coefficient in the bioheat equation // International Journal of Mechanical Sciences. – 2014. – 88. – P. 259-266.

Kaltenbacher B., Klibanov M. An Inverse Problem for a Nonlinear Parabolic Equation with Applications in Population Dynamics and Magnetics // SIAM J. Math. Anal. – 2008. – 39, №6. – P. 1863–1889.

Di Blasio G., Lorenzi A. An Identification Problem in Age-Dependent Population Diffusion //

Numerical Functional Analysis and Optimization. – 2013. – 34, №1. – P. 36-73.

Bouchouev I., Isakov V. The inverse problem of option pricing // Inverse Problems. – 1997. – 13. – P. 7–11.

Kabanikhin S. I. Definitions and examples of inverse and ill-posed problems // J. Inv. Ill-Posed Problems. – 2008. – 16. – P. 317–357.

Saldina N. Inverse problem for a parabolic equation with weak degeneration//Mat. methods and phys.-mech. fields. – 2006. – 49, No. 3. – P. 7–17.

Ivanchov M., Saldina N. Inverse problem for a parabolic equation with strong power-law degeneration // Ukr. Mat. Journal. – 2006. – 58, No. 11. – P. 1487-1500.

Ivanchov M., Saldina N. An inverse problem for strongly degenerate heat equation // J. Inv. Ill-Posed Problems. – 2006. – 14, №5. – С. 465-480.

Cannarsa P., Tort J., Yamamoto M. Determinationofsourcetermsinadegenerateparabolicequation // Inverse Problems. – 2010. – 26, №10. – 105003.

Deng Z., Yang L. An inverse problem of identifying the coefficient of first-order in a degenerate parabolic equation // Journal of Computational and Applied Mathematics. – 2011. – 235. – P. 4404-4417.

Tort J. Determination of source terms in a degenerate parabolic equation from a locally distributed observation // C. R. Acad. Sci. Paris, Ser. I. – 2010. – 348. – P. 1287-1291.

Sagaydak R. On one inverse problem for a two-dimensional equation of parabolic type in a rectangle // Visn. Lviv. Un-tu. Ser. mech.-mat. – 2003. – 62. – P. 117-128.

Baranska I., Ivanchov M. Inverse problem for two-dimensional heat conduction in a region with free boundaries // Ukr. mat. visn. – 2007. – 4, No. 4. – P. 457-484.

Baranska I. Ye. Inverse problem in a region with a free boundary for an anisotropic equation of parabolic type // Naukovyi visnyk Chernivtsi University. – 2008. – 374. – P. 13-29.

Ivanchov M. Inverse problems for equations of parabolic type. — VNTL Publishers, 2003.

Ivanchev M., Vlasov V. Inverse problem for two-dimensional heat equation with weak degeneration // Visn. Lviv. Unv. Ser. Mech.-Mat. – 2009. – 70. – P. 91-102.

Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N. Linear and quasi-linear equations of parabolic type. — M.: Nauka, 1967.