Nonlinear Reaction-Diffusion Equations Used in Modeling Physical Phenomena
Mathematics | Non-linear Dynamics | Statistical, Nonlinear, and Soft Matter Physics
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.
Bricher, Stephen, "Nonlinear Reaction-Diffusion Equations Used in Modeling Physical Phenomena" (2015). Post-Grant Reports. Report. Submission 32.