Mathematics – Analysis of PDEs
Scientific paper
2011-07-11
Mathematics
Analysis of PDEs
Scientific paper
We consider the dynamics of the Total Variation Flow (TVF)
$u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE)
$u_t=\Delta\sign(u)$ in one spatial dimension. We find the explicit dynamic and
sharp asymptotic behaviour for the TVF, and we deduce the one for the SFDE by
an explicit correspondence between the two equations.
Bonforte Matteo
Figalli Alessio
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