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Zbl 1147.35105
Chang, Yu-Hsien; Jau, Guo-Chin; Pao, C.V.
Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer. (English)
[J] Nonlinear Anal., Real World Appl. 9, No. 3, 822-829 (2008). ISSN 1468-1218

Summary: 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 $\sigma $, that a unique bounded global solution exists if $\sigma < \underline \sigma $ and the solution blows up in finite time if $\sigma > \overline \sigma $, where $\underline\sigma < \overline \sigma$. Various estimates for $\overline \sigma$ 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.

MSC 2000:: *35Q80 Appl. of PDE in areas other than physics
35B40 Asymptotic behavior of solutions of PDE
35F30 Boundary value problems for first order nonlinear PDE
80A20 Heat and mass transfer
80A25 Combustion, interior ballistics

Keywords: blowup of solution; global existence; upper and lower solutions; monotone iterations; interphase heat-transfer; ignition time

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Zentralblatt MATH Berlin [Germany]