title: Gelfand-type problem for two-phase porous media.
abstract: 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 uses a 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 owing to the absence of stationary temperature distribution. We also show that the presence of interphase 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.
authors.affiliation: Department of Mathematics , University of Akron , Akron, OH 44325, USA.
authors.forename: Peter V
authors.initials: PV
authors.lastname: Gordon
authors.affiliation: Department of Mathematics , Swansea University , Singleton Park, Swansea SA2 8PP, UK.
authors.forename: Vitaly
authors.initials: V
authors.lastname: Moroz
keywords: Gelfand problem; blow-up; porous media combustion; reaction–diffusion systems; singular limits; thermal explosion