Homogenization of Hamilton - Jacobi Equations

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Sadeghi Arjmand, Saeed | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52248 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi, Morteza
Abstract:
The aim of homogenization theory is to establish the macroscopic behaviour of a system which is ‘microscopically’ heterogeneous, in order to describe some characteristics of the heterogeneous medium (for instance, its thermal or electrical conductivity). This means that the heterogeneous material is replaced by a homogeneous fictitious one (the ‘homogenized’ material), whose global (or overall) characteristics are a good approximation of the initial ones. From the mathematical point of view, this signifies mainly that the solutions of a boundary value problem, depending on a small parameter, converge to the solution of a limit boundary value problem which is explicitly described. In Particular, we focus on Hamilton - Jacobi equations in branch of PDEs
Keywords:
Homogenization ; Hamilton-Jacobi Equation ; Variational Form ; Asymptotic Behavior

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