Layering methods for nonlinear partial differential equations of first order
This paper is concerned with generalized, discontinuous solutions of initial value problems for nonlinear first order partial differential equations. “Layering” is a method of approximating an arbitrary generalized solution by dividing its domain, say a half-space , into thin layers , , and using a strict solution in the -th layer. On the interface , is required to reduce to a smooth function approximating the values on that plane of . The resulting stratified configuration of strict solutions...