Positive Solutions of Semilinear Elliptic Boundary Value Problems in Chemical Reactor Theory

  • Kenichiro Umezu
  • Kazuaki Taira
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)

Abstract

This paper is devoted to the study of semilinear elliptic boundary value problems arising in chemical reactor theory which obey the simple Arrhenius rate law and Newtonian cooling. We prove that ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless heat evolution rate. Moreover the asymptotic behavior of the stable steady temperature is also studied.

Keywords

Elliptic Boundary Unique Positive Solution Newtonian Cool Reactant Consumption Nonlinear Elliptic Boundary 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Kenichiro Umezu
    • 1
  • Kazuaki Taira
    • 2
  1. 1.Maebashi Institute of TechnologyMaebashi 371Japan
  2. 2.Department of MathematicsHiroshima UniversityHigashi-Hiroshima 739Japan

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