On Weak Solutions of von Karmans Equations
Author
Ørtoft, Line
Term
4. term
Education
Publication year
2001
Abstract
Denne afhandling præsenterer og forklarer centrale resultater om von Karman-ligningerne, et koblet system af partielle differentialligninger: én hyperbolisk og én elliptisk. Vi følger Lions’ bevis for, at svage løsninger eksisterer, og beviset af Boutet de Monvel og Chueshov for, at sådanne løsninger er entydige. En svag løsning er en generaliseret løsning, der opfylder ligningerne i en gennemsnitlig, distributionel forstand, når klassiske afledte måske ikke findes. Analysen udføres i rammerne af vektordistributioner og vektorværdige funktioner. De første tre kapitler giver den nødvendige baggrund og værktøjer, før de centrale eksistens- og entydighedsresultater fastlægges.
This thesis presents and explains key results about the von Karman equations, a coupled system of partial differential equations: one hyperbolic and one elliptic. We follow Lions’ proof that weak solutions exist and the proof by Boutet de Monvel and Chueshov that such solutions are unique. A weak solution is a generalized solution that satisfies the equations in an averaged, distributional sense, appropriate when classical derivatives may not exist. The analysis is carried out within the framework of vector distributions and vector-valued functions. The first three chapters provide the necessary background and tools before the main existence and uniqueness results are established.
[This abstract was generated with the help of AI]
Documents