Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II

Autor:	Wilczak, Daniel, Zgliczyński, Piotr
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Analysis of PDEs Mathematics - Numerical Analysis 35B40 35B45 65G30 65N30
Druh dokumentu:	Working Paper
Popis:	We present a new algorithm for the rigorous integration of the variational equation (i.e. producing $\mathcal C^1$ estimates) for a class of dissipative PDEs on the torus. As an application for some parameter value for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we prove the existence of infinite number of homo- and heteroclinic orbits to two periodic orbits. The proof is computer assisted. Comment: 57 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.17087 Zobrazit plný text záznamu View this record from Arxiv