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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Jerrold Bebernes
    • 1
  • David Eberly
    • 2
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of MathematicsUniversity of TexasSan AntonioUSA

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