Total Variation Flow and Sign Fast Diffusion in one dimension

By Matteo Bonforte, Alessio Figalli. 2011

49 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2c91f5d8fa084cf6d48ebf0c380710ffc2493e96

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Juan Luis V'azquez
2. A. Audrito
3. Matteo Bonforte
4. G. Grillo
5. A. Tertikas
6. Stathis Filippas
7. Jean Dolbeault
8. Luis Caffarelli

In Finance

1. Juan Luis V'azquez

In Mathematical Physics

1. Juan Luis V'azquez
2. Matteo Bonforte
3. G. Grillo
4. A. Audrito

Citations in the corpus

• The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “Though it means no flow for positive data, it has an interesting interpretation in terms of total variation flow for signed data, see [40] in 1D and compare with [209].”