How can I use Mathematica to plot the flow of the following ODE in $\mathbb R$? $$\frac{d}{dt} X(t,x) = \chi_{\{x>0\}}(X(t,x)), t \in [0,T],$$ $X(0,x) = x, x \in \mathbb R$
where $\chi$ denotes the indicator function of a set.
I know about the command NDSolve
, but is it applicable in this situation given the discontinuity in the source term? And I'd be mostly interested in rendering a nice picture of the flow.
Note that a related question was posed on MathOverflow.