Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
KeywordsViscous Burgers equation, computer assisted proof, fixed point, dissipative PDE, rigorous numerics, Galerkin projection
AbstractWe 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.
How to Cite
CYRANKA, Jacek. Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof. Topological Methods in Nonlinear Analysis [online]. 1 June 2015, T. 45, nr 2, s. 655–697. [accessed 29.1.2023]. DOI 10.12775/TMNA.2015.031.
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