Existence of a Global Classical Solution of One Problem Arising in Combustion Theory - Borodin, M. A. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
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.