# The Rigid Ignition Model

• Jerrold Bebernes
• David Eberly
Part of the Applied Mathematical Sciences book series (AMS, volume 83)

## Abstract

We wish to analyze indepth the solid fuel ignition model (1.28-)(1.29)
$$\begin{array}{*{20}{c}} {{\theta _t} - \Delta \theta = \delta {e^\theta },{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {x,t} \right) \in \Omega {\mkern 1mu} {\mkern 1mu} \times {\mkern 1mu} {\mkern 1mu} \left( {0,T} \right)} \\ {\theta \left( {x,0} \right) = 0,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} x \in \Omega } \\ {\theta \left( {x,t} \right) = 0,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {x,t} \right) \in \partial \Omega {\mkern 1mu} {\mkern 1mu} \times {\mkern 1mu} {\mkern 1mu} \left( {0,T} \right)} \end{array}$$
and its relationship to the steady-state model (1.30)-(1.31)
$$\begin{array}{*{20}{c}} { - \Delta \psi = \delta {e^\psi },{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} x \in \Omega } \\ {\psi (x) = 0,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} x \in \partial \Omega .} \end{array}$$

## Keywords

Unique Solution Maximum Principle Finite Time Minimal Solution Singular Solution
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