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Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto–Sivashinsky PDE—A Computer-Assisted Proof

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Abstract

We present a method of self-consistent a priori bounds, which allows us to study rigorously the dynamics of dissipative PDEs. As an application we present a computer-assisted proof of the existence of a periodic orbit for the Kuramoto-Sivashinsky equation where ν = 0.127.

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  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków , Poland

    Piotr Zgliczynski

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  1. Piotr Zgliczynski
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Correspondence to Piotr Zgliczynski.

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Zgliczynski, P. Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto–Sivashinsky PDE—A Computer-Assisted Proof. Found Comput Math 4, 157–185 (2004). https://doi.org/10.1007/s10208-002-0080-8

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  • DOI: https://doi.org/10.1007/s10208-002-0080-8

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