Exploratory research project PN-II-ID-PCE-2011-3-0154

        General Information
        Research Team
        Scientific Reports

Project Title:

Qualitative properties of the solution set of differential inclusions

Project number:

244 from 05/10/2011

Project Manager:

Prof. dr. Ovidiu Cârjă

Thematic fields:

11 Main Sciences: Mathematics


This project is motivated by various applications of dynamical systems in wide range of mathematical fields such as in population dynamics, reaction--diffusion processes, qualitative theory in partial differential equations, optimal control theory. The proposed topics refer to problems of flow invariance, stability and control theory of differential inclusions. We study approximate weak and strong invariance for various types of systems, including impulsive differential inclusions and differential inclusions with fractional derivatives. We study regularity properties of the solution map, closely related to the relaxation type theorems and to the celebrated Filippov-Plis estimates. We shall weaken Lipschitz property to Kamke or one sided Lipschitz assumptions on the multifunction. Further, using Lyapunov-like functions, we shall present a characterization of the dynamic of the reachable set, in the case of functional differential inclusions, and derive new uniqueness results for the Funnel Equation. Finally, we continue our previous research concerning the regularity of the minimum time function associated to nonlinear control systems. We analyze the minimum time function in connection with the optimality principle and the corresponding Hamilton-Jacobi-Bellman equation for general differential inclusions in Banach spaces, via contingent solutions.