Abstract / Description of output
For a periodic vector field F, let
Xϵ solve the dynamical system
dXϵdt=F(Xϵϵ).
In \cite{DeGiorgi} Ennio De Giorgi enquiers whether from the existence of the limit X0(t):=limϵ→0Xϵ(t) one can conclude that dX0dt=constant. Our main result settles this conjecture under fairly general assumptions on F, which may also depend on t-variable.
Once the above problem is solved, one can apply the result to the transport equation, in a standard way. This is also touched upon in the text to follow.
Xϵ solve the dynamical system
dXϵdt=F(Xϵϵ).
In \cite{DeGiorgi} Ennio De Giorgi enquiers whether from the existence of the limit X0(t):=limϵ→0Xϵ(t) one can conclude that dX0dt=constant. Our main result settles this conjecture under fairly general assumptions on F, which may also depend on t-variable.
Once the above problem is solved, one can apply the result to the transport equation, in a standard way. This is also touched upon in the text to follow.
| Original language | English |
|---|---|
| Publisher | ArXiv |
| Number of pages | 15 |
| Publication status | Published - 29 Dec 2015 |