On One Nonlocal Problem with Free Boundary - Berezovsky, A. A.; Mitropolskiy, Yu. A.; Netesova, T. M. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We investigate group-theoretic properties of a nonlocal problem with free boundary for a degenerating quasilinear parabolic equation. We establish conditions for the invariant solvability of this problem, perform its reduction, and obtain an exact self-similar solution.