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math.DS2014
Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
Jacek Cyranka, Piotr Zgliczyński
We describe a topological method to study the dynamics of dissipative PDEs on a torus with rapidly oscillating forcing terms. We show that a dissipative PDE, which is invariant wit…
math.DS2014★ 19 cited
Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof
Jacek Cyranka, Piotr Zgliczyński
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 n…
math.DS2013
Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
Jacek Cyranka
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 periodi…