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

Notes

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Graduation Date

2005

Semester

Spring

Advisor

Cannon, John

Degree

Doctor of Philosophy (Ph.D.)

College

College of Arts and Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0000551

URL

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

Language

English

Release Date

May 2005

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Included in

Mathematics Commons

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