Parabolic Systems and an Underlying Lagrangian

by Yolcu, Türkay

Abstract (Summary)
In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L^1.
Bibliographical Information:

Advisor:Chow, Shui-Nee; Gangbo, Wilfrid; Harrell, Evans; Swiech, Andrzej; Yezzi, Anthony Joseph

School:Georgia Institute of Technology

School Location:USA - Georgia

Source Type:Master's Thesis



Date of Publication:07/07/2009

© 2009 All Rights Reserved.