Second microlocal ellipticity and propagation of conormality for semilinear wave equations. (English) Zbl 0746.35021

Sá Barreto, Antônio

J. Funct. Anal. 102, No. 1, 47-71 (1991).

The author considers three problems on the propagation of conormal singularities for semilinear wave equations: the evolution of two simply tangent waves, the interaction of three conormal waves, and the evolution of one wave with a cusp singularity. He uses quasihomogeneous blow-ups to reduce the geometries to normal crossing and show that the lift of the operator by these blow-down maps is elliptic in some directions of the compressed cotangent bundle of the blown-up manifold. This leads to a strengthening of the previously known results and a simplification of their proofs.

Reviewer: Chen Shuxing (Shanghai)

MSC:

35L65	Hyperbolic conservation laws
35A27	Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
58J47	Propagation of singularities; initial value problems on manifolds
35L05	Wave equation

Keywords:

conormal singularities; evolution of two simply tangent waves; interaction of three conormal waves; wave with a cusp singularity; quasihomogeneous blow-ups

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