Semi-linear Cauchy problem with conormal initial data: Regularity at an edge and principal symbol
We consider the semilinear Cauchy problem for a first-order strictly hyperbolic system with any size, any number of variables and (sufficiently regular) conormal initial data with respect to an hypersurface. We precise the conormal structure of the solution and we prove, thanks to a suitable paradifferential calculus, that the principal symbol of the solution coincides, outside the wedge, with the solution of the standard transport equation corresponding formally to the linearized problem.
scientific article; zbMATH DE number 891053