Inverse Problem for a Two-Dimensional Diffusion Equation in a Domain with Free Boundary
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 7, pp 1019-1031.
Citation Example: Ivanchov N. I., Pabyrivs’ka N. V. Inverse Problem for a Two-Dimensional Diffusion Equation in a Domain with Free Boundary // Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 917–927.