This project will involve nonlinear strictly hyperbolic differential equations. We will consider the following problems: estimates for linear equations, decay of solutions, and extension to nonconstant coefficients of results known for the D'Alambertian operator. The studies will include the analysis of the interaction of singularities across nonsmooth surfaces. Further construction of examples exhibiting nonlinear singularities will be attempted. Precise regularity theorems will be developed in order to show that certain explicit approximate solutions differ from the actual ones. Technological developments such as better radars, X-ray devices, and scanners ultimately rely on the understanding of the hyperbolic equations considered in this project.
