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- W4287257407 abstract "We consider the semilinear heat equation with Sobolev subcritical power nonlinearity in dimension $N=2$, and $u(x,t)$ a solution which blows up in finite time $T$. Given a non isolated blow-up point $a$, we assume that the Taylor expansion of the solution near $(a,T)$ obeys some degenerate situation labeled by some even integer $m(a)ge 4$. If we have a sequence $a_n to a$ as $nto infty$, we show after a change of coordinates and the extraction of a subsequence that either $a_{n,1}-a_1 = o((a_{n,2}-a_2)^2)$ or $|a_{n,1}-a_1||a_{n,2}-a_2|^{-beta} |log|a_{n,2}-a_2||^{-alpha} to L> 0$ for some $L>0$, %up to extracting a subsequence still denoted the same, where $alpha$ and $beta$ enjoy a finite number of rational values with $beta in(0,2]$ and $L$ is a solution of a polynomial equation depending on the coefficients of the Taylor expansion of the solution. If $m(a)=4$, then $alpha=0$ and either $beta=3/2$ or $beta =2$." @default.
- W4287257407 created "2022-07-25" @default.
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- W4287257407 date "2021-03-23" @default.
- W4287257407 modified "2023-09-27" @default.
- W4287257407 title "Behavior rigidity near non-isolated blow-up points for the semilinear heat equation" @default.
- W4287257407 doi "https://doi.org/10.48550/arxiv.2103.12795" @default.
- W4287257407 hasPublicationYear "2021" @default.
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