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Saima Gul

Doctor of Philosophy, (Mathematics)
Study Completed: 2019
College of Sciences

Citation

Thesis Title
Differential equations arising in the study of a cell growth model

A class of functional differential equations (FDE) arise in the study of a size structured cell growth model. Ms Gul researched pantograph equations, which arise as separable solutions and developed a novel technique for solving pantograph-type equations. In addition, she considered the cell division model where cells do not divide when they are under a certain size and established the existence and the uniqueness of the solution. She analytically showed there exists an SSD (steady size distribution) solution to this problem. A second order partial differential equation arises when stochasticity exists in the growth rate. Ms Gul solved a second order partial FDE with linear growth rate and showed that as time goes to infinity, this problem does not have an SSD solution. Her research has provided valuable insight and understanding of the existence and uniqueness of the solutions to the cell growth/division model for various growth and division rates.

Supervisors
Associate Professor Bruce Van Brunt
Emeritus Professor Graeme Wake