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| In this talk we consider the Cauchy problem for the convection diffusion equation
$\partial_tu=\Delta u+a\cdot\nabla (|u|^{q-1}u)$ in $(0,\infty)\times{\mathbb R}^n$ with $a\in{\mathbb R}^n$ and $q>1+1/n$, $n\ge 1$, and give more precise asymptotic profiles of the solutions that behaves like the heat kernel as $t\to\infty$, introducing a suitable spatial
shift and correction term. As a corollary we also prove that the decay rates of the difference between the solution and the heat kernel are optimal. |
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