Gradient Flow - Definition and Sources

[muzialis]

Hi all,

I am struggling to find any elementary material on the "gradient flow of a functional" concept.

From introductions in advanced papers I seem to have understood that, assigned a functional F (u), the gradient flow is charactwerized by an equation of the type Du / Dt = P u , where P is a differential operator related to the functional's Euler- Lagrange equation.

I would like to understand more, but was surpsrisngly unable to find any sources on the Internet.
Can anybody suggest a good starting reading?

Many thanks for any help

 

[fresh_42]

I always try to find lecture notes for questions like yours, e.g.
https://www-dimat.unipv.it/savare/pubblicazioni/Daneri-Savare-preprint10.pdf