## Electronic Theses and Dissertations

#### Keywords

Diffusion, Control

#### Abstract

As motivation for the mathematical problems considered in this work, consider a chamber in the form of a long linear transparent tube. We allow for the introduction or removal of material in a gaseous state at the ends of the tube. The material diffuses throughout the tube with or without reaction with other materials. By illuminating the tube on one side with a light source with a frequency range spanning the absorption range for the material and collecting the residual light that passes through the tube with photo-reception equipment, we can obtain a measurement of the total mass of material contained in the tube as a function of time. Using the total mass as switch points for changing the boundary conditions for introduction or removal of material. The objective is to keep the total mass of material in the tube oscillating between two set values such as $m0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t0; \ u(x,0)=0,$ and $u(0,t)=u(1,t)=\psi(t),$ where $\psi(t)=u_0$ for $t_{2k} < t0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\psi(t),$ where $\psi(t)=1$ for $t_{2k} < t0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\phi(t),$ where $a=a(x,t,u)$, and $\phi(t)=1$ for \$t_{2k} < t

2005

Spring

Cannon, John

#### Degree

Doctor of Philosophy (Ph.D.)

#### College

College of Arts and Sciences

Mathematics

Mathematics

application/pdf

CFE0000551

#### URL

http://purl.fcla.edu/fcla/etd/CFE0000550

English

May 2005

None

#### Access Status

Doctoral Dissertation (Open Access)

COinS