P. Zgliczyński

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20002026

most citedHeteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof

108 citations · 347 across the 26 of their papers we have counts for

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3 papers · 1 filter

math.AP2018

On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions

Piotr Kalita, Piotr Zgliczyński

We study the non-autonomously forced Burgers equation $u_{t} (x, t) + u (x, t) u_{x} (x, t) - u_{xx} (x, t) = f (x, t)$ on the space interval $(0, 1)$ with two sets of the boundary conditions:…

math.AP2001★ 5 cited

Trapping regions and an ODE-type proof of the existence and uniqueness theorem for Navier-Stokes equations with periodic boundary conditions on the plane

Piotr Zgliczynski

Using ODE-methods and trapping regions derived by Mattingly and Sinai we give a new proof of the existence and uniqueness of solutions to Navier-Stokes equations with periodic boun…

math.AP2000★ 1 cited

Rigorous Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky equation

P. Zgliczynski, K. Mischaikow

We present a new topological method for the study of the dynamics of dissipative PDE's. The method is based on the concept of the self-consistent apriori bounds, which allows to ju…