Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof

@article{Cyranka2015ExistenceOG,
title={Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof},
author={Jacek Cyranka and Piotr Zgliczynski},
journal={SIAM J. Applied Dynamical Systems},
year={2015},
volume={14},
pages={787-821}
}

We prove the existence of globally attracting solutions of viscous Burgers’ equation with periodic boundary conditions on the interval for some particular choices of viscosity and non-autonomous forcing. The attracting solution is periodic if the forcing is periodic. The method is general and can be applied to other similar partial differential equations. The proof is computer assisted.

Trapping regions and an ODE-type proof of an existence and uniqueness for Navier-Stokes equations with periodic boundary conditions on the plane, Univ. Iag