Abstract
We consider the blow-up problem of a semilinear heat equation, ut = DΔu + up in Ω × (0, TD), ∂u/∂ν(x, t) = 0 on ∂Ω × (0,TD), u(x, 0) = φ(x) ≥ 0 in Ω, where Ω is a bounded smooth domain in RN, TD > 0, D > 0, and p > 1. We study the blow-up time, the location of the blow-up set, and the blow-up profile of the blow-up solution for sufficiently large D. In particular, we prove that, for almost all initial data φ, if D is sufficiently large, then the solution blows-up only near the maximum points of the orthogonal projection of the initial data φ from L2 (Ω) onto the second Neumann eigenspace.
Original language | English |
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Pages (from-to) | 114-128 |
Number of pages | 15 |
Journal | Journal of Differential Equations |
Volume | 212 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2005 May 1 |
Keywords
- Blow-up profile
- Blow-up set
- Blow-up time
- Nonlinear diffusion equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics