**Traveling Wave Solutions of Nonlinear
Diffusion Equations**
**Sumanth Swaminathan **and David Edwards
Department of Mathematics
Polymer-penetrant systems exhibit different behavior from that explained
by the standard diffusion equation:
C_{t}=[D(C)C_{x}]_{x}
These systems come up in membrane production, protective sealants, VLSI
chip etching, drug delivery, and other areas. Some of the unusual
behavior can be explained by a viscoelastic stress ó. Because
the diffusion of the penetrant through the polymer is observed to be abnormal
due to the stress, a new model is proposed for the polymer system involving
two partial differential equations:
C_{t}=[D(C)C_{x} +E(C)Ó_{x} ]_{x}
,
Ó_{t} + B(C) Ó =nC + vC_{t} .
The goal of this project is to find traveling wave solutions that will
profile the change in concentration of the system. The polymer film
is set up as a one dimensional system where concentration of penetrant
and stress vary with position and time. Finding traveling wave solutions
will be essential to the understanding of the partial differential equations. |