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- W3185318444 abstract "Abstract We consider the semilinear heat equation with Sobolev subcritical power nonlinearity in dimension $N=2$, and $u(x,t)$ a solution that 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 $L>0$, 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.
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- W3185318444 date "2021-07-16" @default.
- W3185318444 modified "2023-10-10" @default.
- W3185318444 title "Behavior Rigidity Near Non-Isolated Blow-up Points for the Semilinear Heat Equation" @default.
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- W3185318444 doi "https://doi.org/10.1093/imrn/rnab169" @default.
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