Asymptotic Behavior of Traveling Wave Solutions to Reaction-Diffusion Equations

Linfield College
Talk Abstract
We will discuss travelling wave solutions to reaction-diffusion equations of the form:
$u_t=u_xx+ u^p (1-u^q)$
which can be used as a mathematical model for various biological phenomena, as well as to model problems in combustion theory. We identify conditions on the wave speed so that travelling wave solutions exist for the case $p \geq 1$ and $q \geq 1$. Moreover, we estimate the rate of decay of the travelling wave solutions. When $p > 1$ and $q \geq 1$, this estimate requires center manifold theory because the typical linear methods fail to work. Through the mathematical analysis of reaction diffusion equations, we can gain a better understanding of non-linear dynamical systems and their responses to varying parameters.
Talk Subject
Partial Differential Equations
Time Slot