Abstract
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.
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Borodin, M.A. Existence of a Global Classical Solution of One Problem Arising in Combustion Theory. Ukrainian Mathematical Journal 53, 1583–1596 (2001). https://doi.org/10.1023/A:1015231507876
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DOI: https://doi.org/10.1023/A:1015231507876