We consider general reaction dusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small perturbations. We employ recently developed techniques involving point-wise Green's functions estimates for functional erential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available.
The team's goal was to design a hardware system that combines an ultrasound medical imaging device with additional imaging modalities. This new system will simplify the current procedure for more effective diagnosis, decrease preparation and cleaning times, and improve the experience for the patients.