Duke Mathematical Journal
- Duke Math. J.
- Volume 133, Number 3 (2006), 499-525.
Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation
We consider , a solution of which blows up at some time , where , , and . Under a nondegeneracy condition, we show that the mere hypothesis that the blow-up set is continuous and -dimensional implies that it is . In particular, we compute the principal curvatures and directions of . Moreover, a much more refined blow-up behavior is derived for the solution in terms of the newly exhibited geometric objects. Refined regularity for and refined singular behavior of near are linked through a new mechanism of algebraic cancellations that we explain in detail
Duke Math. J., Volume 133, Number 3 (2006), 499-525.
First available in Project Euclid: 13 June 2006
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Zaag, Hatem. Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation. Duke Math. J. 133 (2006), no. 3, 499--525. doi:10.1215/S0012-7094-06-13333-1. https://projecteuclid.org/euclid.dmj/1150201200