Advances in Differential Equations

Local and global properties of solutions of heat equation with superlinear absorption

Tai Nguyen Phuoc and Laurent Véron

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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.

Article information

Adv. Differential Equations, Volume 16, Number 5/6 (2011), 487-522.

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K58: Semilinear parabolic equations 35K91: Semilinear parabolic equations with Laplacian, bi-Laplacian or poly- Laplacian 35K15: Initial value problems for second-order parabolic equations


Phuoc, Tai Nguyen; Véron, Laurent. Local and global properties of solutions of heat equation with superlinear absorption. Adv. Differential Equations 16 (2011), no. 5/6, 487--522.

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