English

Total Variation Flow and Sign Fast Diffusion in one dimension

Analysis of PDEs 2011-08-18 v2

Abstract

We consider the dynamics of the Total Variation Flow (TVF) ut=÷(Du/Du)u_t=\div(Du/|Du|) and of the Sign Fast Diffusion Equation (SFDE) ut=Δ\sign(u)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.

Cite

@article{arxiv.1107.2153,
  title  = {Total Variation Flow and Sign Fast Diffusion in one dimension},
  author = {Matteo Bonforte and Alessio Figalli},
  journal= {arXiv preprint arXiv:1107.2153},
  year   = {2011}
}
R2 v1 2026-06-21T18:35:16.483Z