Existence and uniqueness for a free boundary problem arising in combustion theory

Abstract

This paper deals with the questions of the existence and uniqueness of solutions to a problem with a conical-shaped free boundary. It is also concerned with providing a complete classification of the solutions to a more abstract Serrin-type free boundary problem. These solutions are proved to be either conical-shaped or planar. Such problems arise in the modelling of premixed equidiffusional Bunsen flames in the limit of high activation energies.