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

• Authors: Aleksander Czechowski , Piotr Zgliczyński
• Languages of publication: PL

Abstracts

PL

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

PL

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

• Publisher: [unknown2]
• Journal: Schedae Informaticae
• Year: 2015
• Volume: 24

Dates

published

2015

online

06 - 07 - 2016

Contributors

author

Aleksander Czechowski

author

Piotr Zgliczyński