Nothing seems to kill it once it seems to take root, my neighbor has it and mows it over, it's like a blanket in his yard, I am costantly fighting the intrusion.
He doesn't seem to understand that aggressive tacktics need to be implemented in order to get rid of it instead of mowing it down and scattering the pieces all over just for them too root and make more.
I am sure his yard is a breeding ground for many unwanted plants growing in other yards...not to mention the type he has growing is just plain ugly!!
I've heard it IS terribly invasive in warmer climates. The fact that pretty much any fragment of any part of the plant is capable of rooting makes it very difficult to eradicate! Mowing probably is not the best control tactic. :)