### Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof

DOI: http://dx.doi.org/10.12775/TMNA.2015.031

#### Abstract

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.

#### Keywords

Viscous Burgers equation; computer assisted proof; fixed point; dissipative PDE; rigorous numerics; Galerkin projection

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