Investigation of Nonlinear Kirchhoff Type Equations

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Ahmadpour Jadehkenari, Mohammad Ali | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44769 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
In this thesis, two kind of Kirchhoff type equations are investigated. for each of them we prove existence and uniqueness of weak solution by letting hypothesizes on problems functions and initial conditions and using Faedo-Galerkin method and some theorems in functional analysis. It is should be mentioned that one of the problems has unique strong solution according to compactness theorems. In the nest step stability of these equations are investigated. for this purpose it is showed that total energy of systems will tend to zero as time goes to infinity. Furthermore at the end of each chapter numerical results are presented to illustrate accuracy of obtained theoretical results. Finally we simulate solution’s shape and show that as it was expected the energy of systems will tend to zero
Keywords:
Weak Solution ; Stability ; Global Solution ; Galerkin Approximation ; Compactness ; Kirchhoff Type Equation