@article{a00d15ed-b96a-4d3e-8264-abf9ebad8087,
author = {Aleksander Czechowski, Piotr Zgliczyński},
title = {Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing},
journal = {Schedae Informaticae},
volume = {2015},
number = {Volume 24},
year = {2016},
issn = {1732-3916},
pages = {143-158},keywords = {Boussinesq equation; ill-posed PDEs; periodic solutions; isolating segments},
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.},
doi = {10.4467/20838476SI.15.014.3486},
url = {https://ejournals.eu/en/journal/schedae-informaticae/article/rigorous-numerics-for-pdes-with-indefinite-tail-existence-of-a-periodic-solution-of-the-boussinesq-equation-with-time-dependent-forcing}
}