FREE-BOUNDARY PROBLEM FOR THE HEAT-EQUATION ARISING IN FLAME PROPAGATION

We introduce a new free-boundary problem for the heat equation, of int erest in combustion theory. It is obtained in the description of lamin ar flames as an asymptotic limit for high activation energy. The probl em asks for the determination of a domain in space-time, Omega subset of R(n) x (0, T), and a function u(x, t) greater than or equal to 0 de fined in Omega such that u(t)= Delta u in Omega, u takes certain initi al conditions, u(x, 0) = u(0)(x) for x is an element of Omega(0) = the ta Omega <intersection of> {t = 0}, and two conditions are satisfied o n the free boundary Gamma = theta Omega <intersection of> {t > 0}: u = 0 and u(v) = -1, where u, denotes the derivative of u along the spati al exterior normal to Gamma. We approximate this problem by means of a certain regularization on the boundary and prove the existence of a w eak solution under suitable assumptions on the initial data.