Inverse Problem for a Two-Dimensional Diffusion Equation in a Domain with Free Boundary - Ivanchov, N. I.; Pabyrivs’ka, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
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.