Ignition regimes of a gas suspension in a vessel with heated walls

existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium

“…It allows to estimate explicitly the critical size of the domain. For the Arrhenius type kinetic with F (u 1 ) = exp(u 1 ), the critical condition obtained above performed for one dimensional domains coincides with previous results [2].…”

“…There is a big physical literature devoted to heat explosion in heterogeneous media (see for example [1,2,6,8,11]). In this paper we study one of the models which describes heat explosion in a non-moving heterogeneous medium consisting of reacting particles surrounded by a gas.…”

“…Heat explosion in a two-phase medium is considered in [6,11] in the case where the gas temperature does not depend on the spatial variable. One dimensional spatial case for a particular form of the non-linearity F (u) = exp(u) is studied numerically in [2]. In this work we consider the multidimensional case for an arbitrary positive function F (u).…”

Stability of stationary solutions for a degenerate parabolic system

“…The theory of heat explosion provides numerous mathematical models (see [2][3][4][5][6], and the references therein). In this work we study a two-temperature model describing heat explosion in a heterogeneous medium consisting of reacting particles surrounded by an inert gas.…”

“…Here u 1 is the temperature of the particles, u 2 is the temperature of the gas, and α is a positive parameter. This model was introduced by Dik & Krainov [6] in the onedimensional case with a particular form of the nonlinearity, F(u 1 ) = e u 1 . We have studied [7] the existence and regularity of stationary solutions in the multi-dimensional case.…”