# differential equations – How to implement limit boundary condition in solving PDE

I have to solve a partial differential equation for a function $$F(x,t)$$ where one of the boundary condition is formulated in terms of a limit:

$$lim_{xrightarrow +infty} e^x partial_xF(x,t)=0$$

Is it possible to implement this as a boundary condition in NDSolve (or possibly NDSolve`FiniteDifferenceDerivative)?