Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof
arXiv:1403.7170
Originality Incremental advance
AI Analysis
Provides a rigorous existence result for attractors in a specific PDE, but the method is generalizable to similar equations.
The authors prove the existence of globally attracting solutions for the viscous Burgers equation with nonautonomous forcing, showing periodicity when forcing is periodic, using a computer-assisted proof.
We prove the existence of globally attracting solutions of the viscous Burgers equation with periodic boundary conditions on the line for some particular choices of viscosity and non-autonomous forcing. The attract- ing 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.