Stability, Bifurcation, and Continuation Theory for Perturbed Sweeping Processes

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dc.contributor.advisorMakarenkov, Oleg
dc.creatorWadippuli Achchige, Lakmi Niwanthi
dc.date.accessioned2021-01-13T17:41:31Z
dc.date.available2021-01-13T17:41:31Z
dc.date.created2018-12
dc.date.issued2018-11-19
dc.date.submittedDecember 2018
dc.date.updated2021-01-13T17:41:31Z
dc.description.abstractThis dissertation is devoted to the development of a qualitative theory of perturbed sweeping processes, which are a combination of differential equations and a moving constraint. The differential equations involved are always assumed Lipschitz continuous. As for the moving constraint, several different situations are addressed: Lipschitz continuous in time, BV-continuous in time, state-dependent, state-independent, with convex interior, with prox-regular interior, bounded in time, periodic in time, almost periodic in time. We prove the existence of local and global solutions as well as boundedness, periodicity, almost periodicity, and asymptotic stability of solutions. Furthermore, we establish results on the occurrence of periodic solutions from a switched boundary equilibrium and on bifurcation of cycles from a regular boundary equilibrium. Concrete examples illustrate the main results of the dissertation.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10735.1/9130
dc.language.isoen
dc.subjectLipschitz spaces
dc.subjectBifurcation theory
dc.subjectStability
dc.titleStability, Bifurcation, and Continuation Theory for Perturbed Sweeping Processes
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.levelDoctoral
thesis.degree.namePHD

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