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

Abstract

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.

38 pages, 1 figure

Cited by in corpus (3)

• Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model
• Validated forward integration scheme for parabolic PDEs via Chebyshev series
• A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory