In this talk I will discuss the local and global well-posedness of coupled non- linear wave equations with damping and supercritical sources. Our interests lie in the interaction between source and damping terms and their influence on the behavior of solutions. I will introduce the method of using the monotone operator theory to obtain the local existence of weak solutions to our system. Also we extend a result by Brezis on convex integrals on Sobolev spaces, which allows us to overcome a major technical difficulty in the proof of the existence of solutions.