Variational Method in the Study of Reaction-Diffusion Equations

Thursday, April 25, 2013 - 10:30am - 12:00pm
Lind 305
Roger Lui (Worcester Polytechnic Institute)
The purpose of this talk is to demonstrate how a variational approach may be used to obtain many of the known results of scalar reaction-diffusion equations. It turns out that traveling wave solutions of such equations correspond to minima of the functional. By solving the Euler-Lagrange equation, one can find, or estimate, the minimum wave speed, which is the same as the asymptotic speed of propagation of solutions of the reaction-diffusion equations. Convergence to traveling wave solutions will also be considered. It is unclear if this method can be used to handle the multi-dimensional case, but it should be able to handle reaction-diffusion systems, where stacked-fronts may occur. This is an ongoing joint work with Professor Hirokazu Ninomiya from Meiji University, Japan.