Propagation of singularities phenomena for equations of tricome type

Abstract

A survey of the author's recent results concerning propagation of singularities phenomena for linear mixed type partial differential equations is given. Results described include the interior effects of nontrapping over compact sets and seudo-convexity and the exhibition of the boundary effects of reflection, diffraction, and trapped gliding rays.Implications of the boundary results for selecting domains which can support solutions with isolated parabolic boundary singularities are given. Applications of the interior phenomena to solvability results are discussed as well as interpretations in the context of semi-Riemannian geometry and general relativity.

Keywords:

• Tricomi type
• propagation phenomena
• solvability
• signature change