Location of Repository

In this paper we study a system of nonlinear parabolic equations representing the evolution of small perturbations in a model<br/>describing the combustion of a porous solid. The novelty of this system rests on allowing the fluid and solid phases to assume different temperatures, as opposed to the well-studied single-temperature model in which heat is assumed to be exchanged at an<br/>infinitely rapid rate. Moreover, the underlying model incorporates fluid creation, as a result of reaction, and this property is inherited by the perturbation system. With respect to important physico-chemical parameters we look for global and blowing-up solutions,<br/>both with and without heat loss and fluid production. In this context, blowup can be identified with thermal runaway, from which <br/>ignition of the porous solid is inferred (a self-sustaining combustion wave is generated). We then proceed to study the existence<br/>and uniqueness of a particular class of steady states and examine their relationship to the corresponding class of time-dependent<br/> problems. This enables us to extend the global-existence results, and to indicate consistency between the time-independent and<br/>time-dependent analyses. In order to better understand the effects of distinct temperatures in each phase, a number of our results are<br/> then compared with those of a corresponding single-temperature model.We find that the results coincide in the appropriate limit of<br/>infinite heat-exchange rate. However, when the heat exchange is finite the blowup results can be altered substantially

Topics:
TP, QA, QC

Year: 2008

OAI identifier:
oai:eprints.soton.ac.uk:44771

Provided by:
e-Prints Soton

Downloaded from
http://dx.doi.org/10.1016/j.nonrwa.2006.12.002

- (1999). An oscillatory route to extinction for solid fuel combustion waves due to heat losses,
- (1999). Analysis of ignition of a porous energetic material,
- (1985). Blowup of positive solutions of semilinear heat equations,
- (1981). Carr,Applications of centre manifold theory,Applied
- (1996). Combustion pseudo-waves,
- (1997). Combustion waves for gases (Le = 1) and solids
- (1977). Criteria for thermal explosions with and without reactant consumption,
- (1987). criterion for blow-up of solutions to semilinear heat equations,
- (1996). Critical values for some non-class A geometries in thermal ignition theory,
- (1955). Diffusion and Heat Transfer in Chemical Kinetics,
- (2003). Effects of gas–solid nonequilibrium in ﬁltration combustion,
- (2000). Effects of vaporization, diffusion and condensation on the combustion of reactive ﬂuids in hot porous media,
- (2001). Elliptic partial differential equations of second order, revised third ed.,
- (1959). Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions,
- (1981). Evolution of a deﬂagration in a cold combustible subjected to a uniform energy ﬂux,
- (2004). G.C.Wake,The existence of steady states to a combustion model with internal heating,
- (2002). Global solutions for quasilinear parabolic problems,
- (1993). Global, unbounded solutions to a parabolic equation,
- (1999). Ignition analysis of a porous energetic material: II. Ignition at a closed heated end,
- (2003). Inﬂuence of subsurface gaseous combustion on the burning of conﬁned porous energetic materials,
- (1993). Initial conditions for thermal ignition,
- (1981). Kassoy,A mathematical analysis of blow-up for thermal runaway,
- (1968). Linear and Quasi-linear Elliptic Equations,Academic Press,
- (1983). Mathematical analysis of thermal runaway for spatially inhomogeneous reactions,
- (1989). Mathematical problems from combustion theory,Applied
- (1984). Maximum Principles in Differential Equations,
- (1972). Monotone methods in nonlinear parabolic and elliptic boundary value problems,
- (1990). Nonlinear Differential Equations and Dynamical Systems,
- (1992). Nonlinear Parabolic and Elliptic Equations,
- (2005). On global existence for semilinear parabolic systems,
- (1963). On the growth of solutions of quasilinear parabolic equations,
- (1969). On the nonlinear equations u +
- (1967). Some positone problems suggested by nonlinear heat generation,
- (1983). Steady states of the reaction-diffusion equations. Parts I, II and III,
- (2007). The effects of gas production and movement on the ignition of porous solids,
- (2004). The ignition of low-exothermicity solids by local heating,
- (1975). The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts,
- (1971). Theory of ignition of a reactive solid by constant energy ﬂux,
- (1973). Topics in Stability and Bifurcation Theory,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.