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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 17 December 2012