Iman Mehrabi Nezhad

Valentina Giangreco, apríl 7, 2019

Málstofa í stærðfræði

Titill: Properties of solution trajectories for a metrically regular generalized equation

Fyrirlesari: Iman Mehrabi Nezhad, HÍ

Staðsetning: VR-II 258
Tími: Fimmtudagur 11. apríl kl. 10.00


The presentation starts from a tangible example, analysis of electrical circuits. Using the circuit theory laws, and considering set-valued maps to model the i-v characteristics of semiconductors like diode, and transistor, a generalized equation is obtained. The main concern of the talk is to investigate how perturbing the input signal will affect the output variables. The problem is studied in two cases: the static case, where the input signal is a DC source; and the dynamic case, where there exists an AC source in the circuit. We will review the electronic part very briefly as we are more interested in the mathematical model.In the static case, the problem can be reduced to the existence or absence of local stability properties of the solution map, or metric regularity for the inverse map. In the dynamic case, using methods of variational analysis and strong metric regularity property of an auxiliary map, we are able to prove the regularity properties of the solution trajectories inherited by the input signal. Furthermore, we establish the existence of continuous solution trajectories for the perturbed problem.