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May/June 2011 Local and global properties of solutions of heat equation with superlinear absorption
Tai Nguyen Phuoc, Laurent Véron
Adv. Differential Equations 16(5/6): 487-522 (May/June 2011).

Abstract

We study the limit when $k\to\infty$ of the solutions of $ \partial_tu-\Delta u+f(u)=0$ in $\mathbb R^N\times (0,\infty)$ with initial data $k\delta$, when $f$ is a positive superlinear increasing function. We prove that there exist essentially three types of possible behaviour according to whether $f^{-1}$ and $F^{-1/2}$ belong or not to $L^1(1,\infty)$, where $F(t)=\int_0^t f(s)ds$. We use these results for providing a new and more general construction of the initial trace and some uniqueness and nonuniqueness results for solutions with unbounded initial data.

Citation

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Tai Nguyen Phuoc. Laurent Véron. "Local and global properties of solutions of heat equation with superlinear absorption." Adv. Differential Equations 16 (5/6) 487 - 522, May/June 2011.

Information

Published: May/June 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1222.35109
MathSciNet: MR2816114

Subjects:
Primary: 35K15, 35K58, 35K91

Rights: Copyright © 2011 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.16 • No. 5/6 • May/June 2011
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