Calculus of Variations and Geometric Measure Theory

M. Bonforte - A. Figalli

Total Variation Flow and Sign Fast Diffusion in one dimension

created by figalli on 13 Jan 2012


Accepted Paper

Inserted: 13 jan 2012
Last Updated: 13 jan 2012

Journal: J. Differential Equations
Year: 2012


We consider the dynamics of the Total Variation Flow (TVF) $u_t=div(Du/
)$ 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.