The main aim of the proposed project is to develop several applications in the framework of generalized
smooth functions (GSF). These functions are useful to describe rapidly changing phenomena such as
breaking of steel structures, switching of electrical circuits, motion through different or granular media,
quantum mechanics, etc. In this setting, new general existence results for differential equations was recently
proved.
In this research proposal, we will consider the following theoretical developments with related applications:
1. Solution of equations using Newton`s method and Pontryagin`s principle for optimal control.
2. Development of mechanics with GSF.
3. Visual representation of GSF by programming a Matlabs toolbox.
Innovative aspects of the proposal are hence a broad development of optimal control theory; an extension of
classical mechanics to models with generalized functions; a flexible and easy-to-use Matlab toolbox to
visualize and enhance intuition of students and researchers in the use and properties of GSF. Potential
users can hence be foreseen both in theoretical and applied mathematics, in physics and engineering
applications.
Primary researchers involved are PhD P. Giordano and Prof. M. Kunzinger. The employment of a PhD
candidate is planned.