Solvability Theorems for Linear Equations of Tricomi Type

For a large class of linear mixed type partial differential equations, theorems on local and semi-global solvability are stated and rely on a prior result of the author about the non-trapping of null-bicharacteristics over compact sets and the theory of H¨ormander. A global solvability result modulo smooth error is demonstrated for a slightly reduced class which includes the equations found most commonly in the literature. The key point is the proof of an additional global convexity property for the bicharacteristic flow which results from the construction of a type of convex hull. All of the results are independent of lower order terms as they depend only on the Hamiltonian system associated to the principal symbol. This independence allows for the interpretation of the results in the context of general relativity and semi-Riemannian geometry