Semilinear hyperbolic problems with source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source. The key idea is to use a transmission problem strategy for the problem with the smooth internal layer. That leads to an anastz different from the obvious candidates. The obvious candidates lead to overdetermined equations for correctors. With the transmission problem strategy we compute infinitely accurate expansions.
A transmission problem for the Timoshenko system with one local Kelvin–Voigt damping and non-smooth coefficient at the interface
