Post-Grant Reports
Title
Nonlinear Reaction-Diffusion Equations Used in Modeling Physical Phenomena
Document Type
Report
Publication Date
1-27-2015
Disciplines
Mathematics | Non-linear Dynamics | Statistical, Nonlinear, and Soft Matter Physics
Abstract
In this project, we discuss traveling wave solutions to reaction-diffusion equations of the form
∂u/∂t = (∂²u/∂x²) + up(1-uq),
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 traveling wave solutions exist for the case p ≥ 1 and q ≥ 1. Moreover, we estimate the rate of decay of traveling wave solutions. When p > 1 and q ≥ 1, this estimate requires center manifold theory because the typical linear methods fail to work.
Recommended Citation
Bricher, Stephen, "Nonlinear Reaction-Diffusion Equations Used in Modeling Physical Phenomena" (2015). Post-Grant Reports. Report. Submission 32.
https://digitalcommons.linfield.edu/facgrants/32
Comments
This research was conducted as part of a Linfield College Student-Faculty Collaborative Research Grant in 2014, funded by the Office of Academic Affairs.
The student collaborator was Malley Nason.