Gelfand-type problem for two-phase porous media

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two phase materials, where, in contrast to the classical Gelfand problem which utilizes single temperature approach, the state of the system is described by two different temperatures. We show that similar to the classical Gelfand problem the thermal explosion occurs...