A Qualitative Study Of The Asymptotically Periodic Curvature Flow Equation In A Banded Region

In this thesis,the curvature flow equation with Neumann boundary conditions and asymptotically periodic coefficients is studied.First,we obtain the existence of local-in-time classical solutions,and we obtain the time-global existence of classical solutions by a uniform priori estimates.Secondly,we consider a series of initial value problems and cor-responding time-global solutions.By a uniform priori estimates,we obtain a subsequence converging to the entire solutions.Then,we prove the uniqueness of the entire solution-s using the renormalization method in the direction of negative infinite time and strong maximum principle.Finally,in order to study the ? limit and a limit of the entire solution-s,we use the renormalization method again.Constructing the renormalization function,making a uniform priori estimates,and taking the convergent subsequence by Cantor di-agonalization method,we get the conclusion that ? limit and a limit of entire solutions are the entire solutions of the corresponding limit problems.We also show that they are the periodic traveling waves.