Lawn edge care

Hi folks, I'm new around here and looking for advice.
We have quite a large area of lawn, it surrounds our whole house in a wavy shape. The lawn is raised anything from4-8 inches from the path level and I'm getting fed up of the wee bits of grass that start growing on the face of the edge. Does anyone know if there is anything I can apply to the edge to stop this happening?
The previous owner used to paint petrol onto the face which kept the grass at bay but at current petrol costs there's no chance! My husband occasionally goes out with the weed burner and burns it but this takes ages and doesn't last long!!
Any advice greatly received!!
--
Julz


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It would seem to me if you have an 8" inch high vertical edge with nothing growing on it and nothing holding it back that it will erode and you'll have dirt on the sidewalk. Why not just keep it trimmed with careful use of a weed whacker? If it was just a few inches high, I'd say install metal edging. If you insist on killing it similar to using gasoline, Roundup or similar will work.
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