Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing

Aleksander Czechowski; Piotr Zgliczyński

Titles

Abstract

We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical periodic solutions in the vicinity of 0. The proof is non-perturbative and relies on construction of periodic isolating segments in the Galerkin projections.

Keywords

Boussinesq equation, ill-posed PDEs, periodic solutions, isolating segments

References

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Information

Information: Schedae Informaticae, 2015, Volume 24, pp. 143 - 158

DOI: https://doi.org/10.4467/20838476SI.15.014.3486

Article type: Original article

Titles:

Polish:

Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing

English:

Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing

Authors

Aleksander Czechowski

https://orcid.org/0000-0002-6054-9842

Delft University of Technology, Delft, The Netherlands

Piotr Zgliczyński

Jagiellonian University in Kraków, Gołębia 24, 31-007 Kraków, Poland

Published at: 11.04.2016

Article status: Open

Licence: None

Percentage share of authors:

Aleksander Czechowski (Author) - 50%

Piotr Zgliczyński (Author) - 50%

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English

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