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- W2963313443 abstract "Let $0le u_0(x)in L^1(mathbb{R}^2)cap L^{infty}(mathbb{R}^2)$ be such that $u_0(x)=u_0(|x|)$ for all $|x|ge r_1$ and is monotone decreasingfor all $|x|ge r_1$ for some constant $r_1>0$ and$mbox{ess}inf_{2{B}_{r_1}(0)}u_0gembox{ess}sup_{R^2setminus B_{r_2}(0)}u_0$ for some constant$r_2>r_1$. Then under some mild decay conditions at infinity onthe initial value $u_0$ we will extend the result of P. Daskalopoulos,M.A. del Pino and N. Sesum [4], [6], and prove thecollapsing behaviour of the maximal solution of theequation $u_t=Deltalog u$ in $mathbb{R}^2times (0,T)$, $u(x,0)=u_0(x)$in $mathbb{R}^2$, near its extinction time $T=int_{R^2}u_0dx/4pi$by a simplified method without using the Hamilton-Yau Harnack inequality." @default.
- W2963313443 created "2019-07-30" @default.
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- W2963313443 date "2012-01-01" @default.
- W2963313443 modified "2023-09-23" @default.
- W2963313443 title "Collasping behaviour of a singular diffusion equation" @default.
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- W2963313443 doi "https://doi.org/10.3934/dcds.2012.32.2165" @default.
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