In my studies on the Ricci flow, I was faced with a problem. To prove the existence and uniqueness of solutions to the Ricci flow, it is proved that the Ricci flow is a Parabolic PDE type. Then one can find that it is weakly parabolic, so short-time existence does not follow from standard parabolic theory and use the DeTurck trick.

I've sought to understand the difference between strongly parabolic and weakly parabolic equations, But did not get a good result. Please guide me.

Thanks!

canbe solved using the standard theory of parabolic PDE's. Also, if you are studying the Ricci flow, I suggest just accepting the result on short time existence and focus on more important aspects. – Deane Yang Apr 4 '13 at 14:20