A transmission problem for quasi-linear wave equations
arXiv:1401.0277 · doi:10.1016/j.jde.2013.12.014
Abstract
We prove the local existence and uniqueness of solutions to a system of quasi-linear wave equations involving a jump discontinuity in the lower order terms. A continuation principle is also established.
The results of this article are essential to a local existence proof of solutions to the Einstein field equations coupled to elastic matter that represent gravitating compact bodies. The full existence proof will be presented in a separate article