On a steady state free boundary problem arising in combustion theory (Q1198678)

The purpose of this paper is to establish the existence of a weak solution of an elliptic free boundary problem arising in the theory of flame propagation. The time independent equations describing the combustion (with constant density) and the model of the flame front as derived by \textit{J. Buckmaster} [e.g.: SIAM J. Appl. Math. 44, 40-55 (1984; Zbl 0536.76098)] is considered. After stating the main assumption and the reformulation of the problem in terms of weak solutions, a nonlinear elliptic problem is investigated. Next, a mixed boundary problem for a second order linear elliptic equation in a piecewise smooth domain is discussed. Finally, the main result is established.