An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle
arXiv:1802.09763 · doi:10.1070/RM2014v069n03ABEH004897
Abstract
We construct an explicit Lyapunov function for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. We assume the nonlinearity is even in the advection term. We follow a method originally suggested by Matano and Zelenyak for, and limited to, separated boundary conditions.
17 pages