I have sent the manuscript of my PhD to the jury today. The thesis speaks about stability and control of quasilinear hyperbolic partial differential equations (for example, stabilization of open channels). I won't speak about it in details here but I can give you the title:
Boundary Stabilization Techniques of Quasi-Linear Hyperbolic Initial-Boundary Value Problem.
Of course, the relation to software testing is not obvious... because there is none.