Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
DOI:
https://doi.org/10.12775/TMNA.2015.031Keywords
Viscous Burgers equation, computer assisted proof, fixed point, dissipative PDE, rigorous numerics, Galerkin projectionAbstract
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.Downloads
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2015-06-01
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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. Vol. 45, no. 2, pp. 655 - 697. [Accessed 14 December 2024]. DOI 10.12775/TMNA.2015.031.
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