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arXiv · 1612.07722

On the perturbed Gelfand equation from combustion theory

Philip Korman·Yi Li·Tiancheng Ouyang
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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 $S$-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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Philip Korman, Yi Li, Tiancheng Ouyang. 2016-12-22. On the perturbed Gelfand equation from combustion theory. https://arxiv.org/abs/1612.07722

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