Date on Master's Thesis/Doctoral Dissertation
8-2017
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
Degree Program
Applied and Industrial Mathematics, PhD
Committee Chair
Xu, Yongzhi
Committee Co-Chair (if applicable)
Swanson, David
Committee Member
Swanson, David
Committee Member
Hu, Changbing
Committee Member
Gie, Gung-Min
Committee Member
Sumanasekera, Gamini
Author's Keywords
partial differential equation; sobolev space; regularization
Abstract
The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential equations (PDE) with terminal conditions are those in which the solution depends uniquely but not continuously on the given condition. In this dissertation, we explore how to find an approximation problem for a nonlinear heat equation which is well-posed. By using a small parameter, we construct an approximation problem and use a modified quasi-boundary value method to regularize a time dependent thermal conductivity heat equation and a quasi-boundary value method to regularize a space dependent thermal conductivity heat equation. Finally we prove, in both cases, the approximation solution converges to the original solution whenever the parameter goes to zero.
Recommended Citation
Hapuarachchi, Sujeewa Indika, "Regularized solutions for terminal problems of parabolic equations." (2017). Electronic Theses and Dissertations. Paper 2776.
https://doi.org/10.18297/etd/2776
