Abstract
This paper is concerned with positive solutions of semilinear diffusion equations in with small diffusion under the Neumann boundary condition, where is a constant and is a bounded domain in with boundary. For the ordinary differential equation , the solution with positive initial data has a blow-up set and a blowup profile outside the blow-up set . For the diffusion equation in under the boundary condition on , it is shown that if a positive function satisfies on , then the blow-up profile of the solution with initial data approaches uniformly on compact sets of as .
Citation
Hiroki YAGISITA. "Blow-up profile of a solution for a nonlinear heat equation with small diffusion." J. Math. Soc. Japan 56 (4) 993 - 1005, October, 2004. https://doi.org/10.2969/jmsj/1190905445
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