Content area
Abstract
Our research focuses on second order nonlinear elliptic partial differential equations, specifically an Allen-Cahn type problem. Using variational methods, we locate known numerical solutions to this equation by finding minima of a related functional. This analysis utilizes a steepest descent program. Since these solutions are distinct, we may employ the Mountain Pass Algorithm, introduced by Choi and McKenna in 1993, to find additional solutions corresponding to saddle points of the functional. We then investigate the qualitative properties of these solutions.
Details
Title
Numerical solutions to an Allen-Cahn type equation
Author
Speicher, Regina
Year
2005
ISBN
978-0-542-30481-1
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
305009785
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
