Until recently, most people have simply sprayed situations like this with Round-Up or other glyphosate based weed killers.
Knock down, leaf active weed killers like glyphosate only kill weeds which are present at the time of spraying. Soon after spraying, new seeds germinate and before too long the area is weedy again.
Recently a new product has been released which can be mixed with glyphosate based weed kiilers or applied to bare ground. This product known as Weed Stop herbicide, forms a protective barrier in the soil and acts on germinating seeds. Weed control can last as long as 9 months thereby significantly reducing the number of sprays to only once or twice per year!
To find out more about new Weed Stop herbicide and view a 2 minute video clip click on this LINK