Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer

Yu Hsien Chang, Guo Chin Jau, C. V. Pao

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper we investigate the blowup property and global existence of a solution for a coupled system of first-order partial differential equation and ordinary differential equation which arises from a catalytic converter in automobile engineering. It is shown, in terms of a single physical parameter σ, that a unique bounded global solution exists if σ < under(σ, {combining low line}) and the solution blows up in finite time if σ > over(σ, -), where under(σ, {combining low line}) < over(σ, -). Various estimates for over(σ, -) and its associate blow-up time T* are explicitly given. The value of T* can be used to estimate the ignition time and ignition length of the ignition system which is an important concern in automobile engineering.

Original languageEnglish
Pages (from-to)822-829
Number of pages8
JournalNonlinear Analysis: Real World Applications
Volume9
Issue number3
DOIs
Publication statusPublished - 2008 Jul 1

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Keywords

  • Blowup of solution
  • Global existence
  • Ignition time
  • Interphase heat-transfer
  • Monotone iterations
  • Upper and lower solutions

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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