Pabyrivs’ka N. V.
Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 917–927
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.
Simultaneous Determination of Two Coefficients of a Parabolic Equation in the Case of Nonlocal and Integral Conditions
Ukr. Mat. Zh. - 2001. - 53, № 5. - pp. 589-596
We establish conditions for the existence and uniqueness of a solution of the inverse problem for a parabolic equation with two unknown time-dependent coefficients in the case of nonlocal boundary conditions and integral overdetermination conditions.