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Microlocal analysis and global solutions of some hyperbolic equations with discontinuous coefficients. (English) Zbl 0998.46016

Hyperbolic partial differential equations with distributional coefficients are treated in the class of Colombeau distributions. The coefficients have jump discontinuities and partial differential equations of this type were analyzed before concerning existence of global distributional solutions. In the framework of Colombeau distributions a refined notion of wave-front sets is employed to allow for microlocal analysis.

MSC:

46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
35L45 Initial value problems for first-order hyperbolic systems
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