Descript 
88 p 
Note 
Source: Dissertation Abstracts International, Volume: 6608, Section: B, page: 4263 

Adviser: Rafe Mazzeo 

Thesis (Ph.D.)Stanford University, 2005 

This thesis presents a method to represent curves evolving under curve shortening flow as nodal sets of the limit of solutions to the parabolic GinzburgLandau equation 

Consider family of compact curves Gamma(lambda,t) : [0, lambda) x [0, T) → R2 that depend on a time parameter t, have an extinction time T and satisfy the equation 6G6t l,t=kGn&d4; , 1 where kGamma is the spatial curvature of Gamma(lambda, t) and nˆ its unit normal 

Let u* be a solution to u*xx +12W' u*=0 u*0= 0andlim x→+/infinityu* x=+/1 

I construct a family of solutions to the parabolic GinzburgLandau equation: 6ue6t Due+1 uWue 2e2 =0 2 such that lime→0 supx ,t∈R2x &sqbl0;0,infinity&parr0; uex,t v&d5;*e x,t=0, where v&d5;*e is a function with the following features: 

Let d(x, t) be the signed distance to Gamma(lambda, t). Then for t < T there are neighborhoods U ' ⊂ U of Gamma(lambda, t) such that v&d5;*e x,t=u* dx,t e forx∈U', and v&d5;*e x,t≡ 1forx∈R 2\U 

For t ≥ T v&d5;*e x,t≡1 

This result is proven by constructing approximate solutions v&d5;*e to the equation (2) and estimating epsilon( x, t)  v&d5;*e (x, t) using fixed point methods 

School code: 0212 

DDC 
Host Item 
Dissertation Abstracts International 6608B

Subject 
Mathematics


0405

Alt Author 
Stanford University

