#### Faculty Sponsor(s)

Stephen Bricher

#### Location

Jereld R. Nicholson Library

#### Subject Area

Mathematics

#### Description

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 ≥1 and q ≥1. Moreover, we estimate the rate of decay of the travelling wave solutions. When p > 1 and q ≥1, this estimate requires center manifold theory because the typical linear methods fail to work. Through the mathematical analysis of reaction diffusion equations, the results of this research create further studies and application in physical and industrial chemistry.

#### Recommended Citation

Nason, Malley M., "Asymptotic Behavior of Traveling Wave Solutions to Reaction-Diffusion Equations" (2015). *Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement.* Event. Submission 10.

https://digitalcommons.linfield.edu/symposium/2015/all/10

Asymptotic Behavior of Traveling Wave Solutions to Reaction-Diffusion Equations

Jereld R. Nicholson Library

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 ≥1 and q ≥1. Moreover, we estimate the rate of decay of the travelling wave solutions. When p > 1 and q ≥1, this estimate requires center manifold theory because the typical linear methods fail to work. Through the mathematical analysis of reaction diffusion equations, the results of this research create further studies and application in physical and industrial chemistry.