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• W3033960088 abstract "For a smooth bounded domain $Omegasubseteqmathbb{R}^n$, $ngeq 3$, we consider the fast diffusion equation with critical sobolev exponent $$frac{partial w}{partialtau} =Delta w^{frac{n-2}{n+2}}$$ under Dirichlet boundary condition $w(cdot, tau) = 0$ on $partialOmega$. Using the parabolic gluing method, we prove existence of an initial data $w_0$ such that the corresponding solution has extinction rate of the form $$|w(cdot, tau)|_{L^infty(Omega)} = gamma_0(T-tau)^{frac{n+2}{4}}left|ln(T-tau)right|^{frac{n+2}{2(n-2)}}(1+o(1))$$ as $tto T^-$, here $T > 0$ is the finite extinction time of $w(x, tau)$. This generalizes and provides rigorous proof of a result of Galaktionov and King cite{galaktionov2001fast} for the radially symmetric case $Omega =B_1(0) : = {xin mathbb{R}^n||x| < 1}subsetmathbb{R}^n$." @default.
• W3033960088 created "2020-06-12" @default.
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• W3033960088 date "2020-06-01" @default.
• W3033960088 modified "2023-09-27" @default.
• W3033960088 title "Extinction behaviour for the fast diffusion equations with critical exponent and Dirichlet boundary conditions" @default.
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• W3033960088 hasPublicationYear "2020" @default.
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