Adler, J.; Nhamburo, P. T. The critical conditions in a reactive slab with slowly varying surface temperature. (English) Zbl 0674.35040 IMA J. Appl. Math. 35, 265-272 (1985). Summary: Liouville’s nonlinear partial differential equation is considered for an infinite rectangular strip domain with a slowly varying boundary condition. The equation describes a layer of chemically reactive material under conditions where the resistance to surface heat transfer is negligible and the ambient temperature varies slowly along the surface. Symmetrical heating by a zero order exothermic reaction is assumed. If \(\epsilon\) is a small dimensionless temperature difference between regions where the surface temperature is effectively constant, a perturbation series solution in \(\epsilon\) may be determined provided the Frank-Kamenetskij parameter \(\delta\) satisfies \(\delta \leq \delta_ c(\epsilon)\). It is shown that a plausible value for the critical parameter is \(\delta_ c(\epsilon)=\delta_ c(0)e^{-\epsilon},\) where \(\delta_ c(0)=0.878\). The corresponding critical temperature distribution is shown to have a dependence on \(\epsilon\) different from that for subcritical cases. Cited in 2 Documents MSC: 35K55 Nonlinear parabolic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 80A20 Heat and mass transfer, heat flow (MSC2010) 35B20 Perturbations in context of PDEs Keywords:Liouville’s nonlinear partial differential equation; infinite rectangular strip; varying boundary condition; chemically reactive material; perturbation series; Frank-Kamenetskij parameter PDFBibTeX XMLCite \textit{J. Adler} and \textit{P. T. Nhamburo}, IMA J. Appl. Math. 35, 265--272 (1985; Zbl 0674.35040) Full Text: DOI