In article , Franz Heymann notfranz.
writes

I suggest that your only hope is to apply doses of glyphosate at about
three-weekly intervals until you have beaten them. But you will have
to make sure that you treat the complete patches of the weeds, and not
just the psarts which are invading your garden.

Except that glyphosate is translocated within the plant, surely? So
treating the bit in the garden would cause all the plant to die, even
that which was outside the garden. You would still have to treat each
new plant which showed its head within the garden, so it would probably
be an annual job.

Japanese knotweed is a pig to get rid of, and I think there are
restrictions on how you get rid of the bits - search the DEFRA site for
more info. Cutting off each new shoot as soon as it appears worked for
me on a small patch, pouring glyphosate down the cut off shoot might be
an added precaution.
--
Kay
"Do not insult the crocodile until you have crossed the river"