On the perturbed Gelfand equation from combustion theory
Philip Korman, Yi Li, Tiancheng Ouyang
TL;DR
This paper provides a simplified proof and extensions for the S-shaped solution curve of the perturbed Gelfand equation in two dimensions, relevant to combustion theory, confirming the solution structure for small secondary parameters.
Contribution
It offers a simplified proof and extends the understanding of the solution curve structure for the perturbed Gelfand equation in combustion models.
Findings
Confirmed S-shaped solution curve for small secondary parameters
Provided a simplified proof of existing results
Extended the analysis to broader conditions
Abstract
For the perturbed Gelfand's equation on the unit ball in two dimensions, Y. Du and Y. Lou [4] proved that the curve of positive solutions is exactly -shaped, for sufficiently small values of the secondary parameter. We present a simplified proof and some extensions. This problem is prominent in combustion theory, see e.g., the book of J. Bebernes and D. Eberly [1].
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Taxonomy
TopicsNonlinear Partial Differential Equations · Differential Equations and Numerical Methods · Nonlinear Differential Equations Analysis