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Long Time Behavior of Solutions of Hamilton-Jacobi Equations with Time Periodic Hamiltonians

Author: WangChao
Tutor: PuDaXiong
School: Ocean University of China
Course: Applied Mathematics
Keywords: Hamilton-Jacobi equation Asymptotic solution Weak KAM theory Viscosity solution of the time period Aubry set
CLC: O175
Type: Master's thesis
Year: 2010
Downloads: 23
Quote: 0
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Abstract


In this paper, the dynamics of the time period in the whole space Rn viscosity solution of the Hamilton-Jacobi equation for a long time asymptotic behavior of the Preface section describes the basic assumption of this paper , the Hamilton - Jacobi equation solution for a long time asymptotic behavior of research content as well as the latest research developments and results. first chapter introduces the points prior knowledge , need a few basic theorems second chapter studies the fundamental nature of the time period of the Hamilton-Jacobi equation to the first a period of time Hamilton-Jacobi equations viscosity solution existence theorem , and then construct a periodic solution of equation and prove the existence of periodic solution of the extremal curve . third chapter study time period Hamilton-Jacobi equations convergence problems . Firstly, as n → ∞ , u ( x , tn ) three convergence criterion , then prove the theorem of the solution converges to a periodic solution , the last two cycles asymptotic solution expression.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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