Nonconvex Integro-Differential Sweeping Process with Applications
Abderrahim Bouach, Tahar Haddad, Lionel Thibault
Abstract
In this paper, we analyze and discuss the well-posedness of a new variant of the so-called sweeping process. In this variant, the prox-regular moving set $C(t)$ is supposed to have an absolutely continuous variation and is perturbed by an integral forcing term. The integrand of the forcing term depends on two time-variables; that is, we study a general integro-differential sweeping process of Volterra type. The results are applied to nonregular electrical circuits containing time-varying capacitors and nonsmooth electronic devices like diodes. A circuit with transmission line, diode, and inductor is also analyzed. All these applications represent an additional novelty of our paper.
Topics & Concepts
MathematicsForcing (mathematics)CapacitorDiodeElectronic circuitProcess (computing)Term (time)Differential (mechanical device)NoveltyControl theory (sociology)Transmission lineInductorSet (abstract data type)Applied mathematicsTopology (electrical circuits)Mathematical analysisVoltageComputer scienceElectrical engineeringTelecommunicationsCombinatoricsProgramming languageEngineeringOperating systemQuantum mechanicsArtificial intelligencePhilosophyControl (management)TheologyAerospace engineeringPhysicsOptimization and Variational AnalysisNonlinear Differential Equations AnalysisStability and Controllability of Differential Equations