It's like bermuda grass, rhyzomes under ground. My neighbor has them and does not water them, I water my plants and they come over to drink. Stop watering? It's ruellea.

It's a very invasive weed with pretty flowers. Spreads underground, so burying a 12" barrier might work.

If it is surrounded by dry dirt it usually doesn't spread into dry dirt, but next to a lawn it's hopeless.

Just keep mowing it down.

Not only rhizomes, when the seed pods pop they throw the seeds quite a ways. Roundup or similar will knock it down. I keep breaking off the tops and eventually the roots run out of energy to throw out new growth.

Ruellia simply refuse to die! Don't even bother trying to dig it out. You think you have all the roots, but there it is again! Must be kissing cousins to bermuda grass.

Roundup, or just let it keep growing. The young plants are tender and soft, but when it gets older it can be very hard and tough, hard on your mower. That piece that keeps coming back and keeps getting mowed down will get tough like that.