@article{Cyranka_2015, title={Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof}, volume={45}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2015.031}, DOI={10.12775/TMNA.2015.031}, abstractNote={We present a computer assisted method for proving the existence of globally attracting fixed points of dissipative PDEs. An application to the viscous Burgers equation with periodic boundary conditions and a forcing function constant in time is presented as a case study. We establish the existence of a locally attracting fixed point by using rigorous numerics techniques. To prove that the fixed point is, in fact, globally attracting we introduce a technique relying on a construction of an absorbing set, capturing any sufficiently regular initial condition after a finite time. Then the absorbing set is rigorously integrated forward in time to verify that any sufficiently regular initial condition is in the basin of attraction of the fixed point.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Cyranka, Jacek}, year={2015}, month={Jun.}, pages={655–697} }