Optimal control in nonlinear elliptic systems

Shape models based on elliptic PDES, associated energies, and their applications in 2D and 3D Gençtav, Aslı; Tarı, Zehra Sibel; Can, Tolga; Department of Computer Engineering (2018) By using an elliptic PDE or its modifications, we develop implicit shape representations and demonstrate their two- and three-dimensional applications. In the first part of the thesis, we present a novel shape characterization field that provides a local measure of roundness at each shape point. The field is computed by comparing the solution of the elliptic PDE on the shape domain and the solution of the same PDE on the reference disk. We demonstrate its potential via illustrative applications including gl...
Periodic solutions and stability of linear impulsive delay differential equations ALZabut, Jehad; Ağacık, Zafer; Department of Mathematics (2004) In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron co...
Boundary value problems for higher order linear impulsive differential equations Uğur, Ömür; Akhmet, Marat; Taşeli, Hasan; Department of Mathematics (2003) The theory of impulsive di®erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di®erential equations. In this work, higher order linear impulsive equations at xed moments of impulses together with certain boundary conditions are investigated...
Mathematical modelling of enzymatic reactions, simulation and parameter estimation Özöğür, Süreyya; Karasözen, Bülent; Department of Scientific Computing (2005) A deep and analytical understanding of the human metabolism grabbed attention of scientists from biology, medicine and pharmacy. Mathematical models of metabolic pathways offer several advances for this deep and analytical understanding due to their incompensable potential in predicting metabolic processes and anticipating appropriate interventions when required. This thesis concerns mathematical modeling analysis and simulation of metabolic pathways. These pathways include intracellular and extracellular c...
Global behavior of solutions of the Brinkman-Forchheimer equations Uğurlu, Davut; Çelebi, Okay; Kalantarov, Varga; Department of Mathematics (2001)

Citation Formats

K. Leblebicioğlu, “Optimal control in nonlinear elliptic systems,” Ph.D. - Doctoral Program, Middle East Technical University, 1988.