Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 56, Number 4 (2004), 993-1005.
Blow-up profile of a solution for a nonlinear heat equation with small diffusion
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 .
J. Math. Soc. Japan, Volume 56, Number 4 (2004), 993-1005.
First available in Project Euclid: 27 September 2007
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B25: Singular perturbations 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B40: Asymptotic behavior of solutions 35B50: Maximum principles
YAGISITA, Hiroki. Blow-up profile of a solution for a nonlinear heat equation with small diffusion. J. Math. Soc. Japan 56 (2004), no. 4, 993--1005. doi:10.2969/jmsj/1190905445. https://projecteuclid.org/euclid.jmsj/1190905445