  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
exclusively due to the absence of stationary temperature distribution. We also
show that the presence of inter-phase heat exchange delays a thermal explosion.
Moreover, we prove that in the limit of infinite heat exchange between phases
the problem of thermal explosion in two phase porous media reduces to the
classical Gelfand problem with renormalized constants.
