This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. The problem in the first paper is one-dimensional; with one boundary condition given by an integral. The problem in the second paper is three-dimensional, and Dirichlet boundary conditions are used. Both problems have their origins in fluid dynamics. Paper III describes an inverse problem for the heat equation. Given the solution, a solution dependent diffusion coefficient is estimated by intervals at a finite set of points. The method includes the construction of set-valued level curves and two-dimensional splines. In paper IV we prove that there exists a unique, globally attracting fixed point for a differential equation system. The differential equation system arises as the number of peers in a peer-to-peer network, which is described by a suitably scaled Markov chain, goes to infinity. In the proof linearization and Dulac's criterion are used.
Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-161314 |
Date | January 2012 |
Creators | Fogelklou, Oswald |
Publisher | Uppsala universitet, Analys och tillämpad matematik, Uppsala : Department of Mathematics |
Source Sets | DiVA Archive at Upsalla University |
Language | English |
Detected Language | English |
Type | Doctoral thesis, comprehensive summary, info:eu-repo/semantics/doctoralThesis, text |
Format | application/pdf |
Rights | info:eu-repo/semantics/openAccess |
Relation | Uppsala Dissertations in Mathematics, 1401-2049 ; 76 |
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