Borodin M. A.
Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1309-1319
We consider a multidimensional free-boundary problem for a parabolic equation that arises in combustion theory. We prove the existence of a global classical solution. The idea of the method is as follows: first, we perform the differential–difference approximation of the problem and establish its solvability; then we prove uniform estimates and perform a limit transition.
Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 158–167
The existence of the classical solution of the many-dimensional two-phase Stefan problem is proved for any finite time interval in the case of contact of an unknown (free) boundary with the known one.
Ukr. Mat. Zh. - 1992. - 44, № 12. - pp. 1652–1657
Ukr. Mat. Zh. - 1969. - 21, № 2. - pp. 238–246