Inverse problem for a two-dimensional diffusion equation in a domain with free boundary. (English. Ukrainian original) Zbl 1295.35382
Ukr. Math. J. 65, No. 7, 1019-1031 (2013); translation from Ukr. Mat. Zh. 65, No. 7, 917-927 (2013).
Summary: We establish conditions for the existence and uniqueness of a smooth solution to the inverse problem for a two-dimensional diffusion equation with unknown time-dependent leading coefficient in a domain with free-boundary. The equation of unknown boundary is given in the form of the product of a known function of space variables and an unknown time-dependent function.
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