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

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
Full Text: DOI
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