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
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. https://doi.org/10.57262/ade/1355703298
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