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

6 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 language English 822-829 8 Nonlinear Analysis: Real World Applications 9 3 https://doi.org/10.1016/j.nonrwa.2007.01.002 Published - 2008 Jul 1

Fingerprint

Automotive engineering
Catalytic converters
Ignition
Converter
Global Existence
Blow-up
Heat Transfer
Existence of Solutions
Automobile
Heat transfer
Ignition systems
Ordinary differential equations
Partial differential equations
Engineering
Blow-up Time
First order differential equation
Global Solution
Estimate
Coupled System
Ordinary differential equation

Keywords

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

ASJC Scopus subject areas

• Analysis
• Applied Mathematics
• Mathematics(all)
• Modelling and Simulation
• Engineering (miscellaneous)

Cite this

Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer. / Chang, Yu Hsien; Jau, Guo Chin; Pao, C. V.

In: Nonlinear Analysis: Real World Applications, Vol. 9, No. 3, 01.07.2008, p. 822-829.

Research output: Contribution to journalArticle

title = "Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer",
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.",
keywords = "Blowup of solution, Global existence, Ignition time, Interphase heat-transfer, Monotone iterations, Upper and lower solutions",
author = "Chang, {Yu Hsien} and Jau, {Guo Chin} and Pao, {C. V.}",
year = "2008",
month = "7",
day = "1",
doi = "10.1016/j.nonrwa.2007.01.002",
language = "English",
volume = "9",
pages = "822--829",
journal = "Nonlinear Analysis: Real World Applications",
issn = "1468-1218",
publisher = "Elsevier BV",
number = "3",

}

TY - JOUR

T1 - Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer

AU - Chang, Yu Hsien

AU - Jau, Guo Chin

AU - Pao, C. V.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - 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.

AB - 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.

KW - Blowup of solution

KW - Global existence

KW - Ignition time

KW - Interphase heat-transfer

KW - Monotone iterations

KW - Upper and lower solutions

UR - http://www.scopus.com/inward/record.url?scp=38949110317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38949110317&partnerID=8YFLogxK

U2 - 10.1016/j.nonrwa.2007.01.002

DO - 10.1016/j.nonrwa.2007.01.002

M3 - Article

VL - 9

SP - 822

EP - 829

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

IS - 3

ER -