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15 June 2006 Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation
Hatem Zaag
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Duke Math. J. 133(3): 499-525 (15 June 2006). DOI: 10.1215/S0012-7094-06-13333-1

Abstract

We consider u(x,t), a solution of ut=Δu+|u|p1u which blows up at some time T>0, where u:RN×[0,T)R, p>1, and (N2)p<N+2. Under a nondegeneracy condition, we show that the mere hypothesis that the blow-up set S is continuous and (N1)-dimensional implies that it is C2. In particular, we compute the N1 principal curvatures and directions of S. Moreover, a much more refined blow-up behavior is derived for the solution in terms of the newly exhibited geometric objects. Refined regularity for S and refined singular behavior of u near S are linked through a new mechanism of algebraic cancellations that we explain in detail

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Hatem Zaag. "Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation." Duke Math. J. 133 (3) 499 - 525, 15 June 2006. https://doi.org/10.1215/S0012-7094-06-13333-1

Information

Published: 15 June 2006
First available in Project Euclid: 13 June 2006

zbMATH: 1096.35062
MathSciNet: MR2228461
Digital Object Identifier: 10.1215/S0012-7094-06-13333-1

Subjects:
Primary: 35A20 , 35B40
Secondary: 35K55

Rights: Copyright © 2006 Duke University Press

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Vol.133 • No. 3 • 15 June 2006
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